New Families of Binary Sequences with Low Correlation and Large Size

In this paper, a new family of binary sequences of period 2n-1 with low correlation is proposed for integer n = em and even m. The new family has family size 2n + 1 and maximum nontrivial correlation 2n+e/2 + 1 and 2n+e-1/2 + 1 for even and odd e respectively. Especially, for n = 2m and 3m, we obtain a new family of binary sequences with maximum nontrivial correlation 2n/2 + 1 + 1, and the obtained family is one of the binary families with best correlation among the known families with family size no less than their period 2n-1 for even n. Moreover, the correlation distribution of the new family is also determined.

For odd prime p, two new p-ary sequence families with period pn−1 are constructed for odd n=2l+1=me and even n=2l=me respectively. It is shown that, for a given integer ρ, the proposed sequence families have maximum correlation 1+pn/2+(ρ−1)e+1, family size (pn−1)pnρ/2, and maximum linear span n(n+3).

The Gold sequence family [1] is one of the oldest and most well‐known families of binary sequences with optimal correlation properties. This chapter focuses on the binary Gold sequences and their relatives called Gold‐like sequences. Mathematical representations as well as the family sizes and maximum correlation magnitudes of these sequences are reviewed.

A new family of binary sequences with low 4-value autocorrelation of length 4p based on cyclotomic classes of order four is proposed, as well as the linear complexity and 2-adic complexity of these sequences are determined. The results show that the linear complexity of s is LC(s) = 4p−1, and the 2-adic complexity of s is Φ2s = log2 ((24p−1)/3), both of which are greater than half of the period. The sequences are safe enough to resist Berlekamp–Massey algorithm attacks and rational approximation algorithm attacks, which indicate that they are good sequences in communication.

In direct-sequence code-division multiple-access (DS-CDMA) communication systems and direct-sequence ultra wideband (DS-UWB) radios, sequences with low correlation and large family size are important for reducing multiple access interference (MAI) and accepting more active users, respectively. In this paper, a new collection of families of sequences of length pn-1, which includes three constructions, is proposed. The maximum number of cyclically distinct families without GMW sequences in each construction is π(pn-1)/n · π(pm-1)/ m, where p is a prime number, n is an even number, and n = 2m, and these sequences can be binary or polyphase depending upon choice of the parameter p. In Construction I, there are pn distinct sequences within each family and the new sequences have at most d + 2 nontrivial periodic correlation {-pm-1, -1, pm-1,2pm-1,···,dpm-1}. In Construction II, the new sequences have large family size p2n and possibly take the nontrivial correlation values in {-pm-1, -1, pm-1, 2pm-1,···,(3d-4)pm-1}. In Construction III, the new sequences possess the largest family size p(d-1)n and have at most 2d correlation levels {-pm-1, -1, pm-1,2pm-1, ···,(2d-2)pm-1}. Three constructions are near-optimal with respect to the Welch bound because the values of their Welch-Ratios are moderate, WR ≐ d, WR ≐ 3d-4 and WR ≐ 2d-2, respectively. Each family in Constructions I, II and III contains a GMW sequence. In addition, Helleseth sequences and Niho sequences are special cases in Constructions I and III, and their restriction conditions to the integers m and n, pm ≠ 2 (mod 3) and n ≡ 0 (mod 4), respectively, are removed in our sequences. Our sequences in Construction III include the sequences with Niho type decimation 3 · 2m-2, too. Finally, some open questions are pointed out and an example that illustrates the performance of these sequences is given.

The livelihood diversification significantly contributes to the family income having effect on food varieties' consumption in rural families of different sizes. This study investigated the food intake differences among rural families considering different income levels and family sizes. Moreover, barriers faced by the rural families to increase the consumption of food varieties were also analysed. A total of 200 rural families were selected through multistage purposive and random sampling techniques in the Punjab province of Pakistan and were directly interviewed and categorized first into low and high livelihood diversified families. The food groups were derived by assigning individual food to conventional food group taxonomies, and two‐way ANOVA (4 (income groups) × 3 (family size groups) was separately conducted for low and high livelihood diversified families. The income instability, prices of food items, market distance and storage were perceived as barriers for increasing food consumption. The high livelihood diversified families significantly and regularly consumed more food items than low diversified families. The rural households both in low and high livelihood diversified family categories having low income and high family size consumed less expensive food items. The regular consumption of fruits, bakery products, and livestock and dairy items was greatly associated with high income and small family size. One of the most remarkable findings of the multivariate multiple regression model was the households belonging to the lowest income group were significantly lowering the consumption of livestock and dairy food items as the family size increased from small to large family size. The interaction effect was highly associated with per capita income because the consumption of food items increased with the rise in income irrespective of the family size. However, family size groups showed different patterns of food intakes with different income levels. Government agencies should assist rural households to diversify their income portfolios for better nutrition.

In many developing countries, population expansion and high fertility rates have been of concern to individuals, society, and governments. Zambia is one of the countries in sub-Saharan Africa, which has been experiencing high fertility for more than four decades since it attained independence. Understanding of factors associated with desired family size, especially amongst young women, is important because their future reproductive behaviour has the potential to influence the country’s course of fertility. Therefore, this study was conducted to examine the determinants of family size choice among young women in Zambia. The study analysed data extracted from repeated cross-sectional surveys conducted in 2007, 2013 and 2018. The analysis was done on a pooled weighted sample of 15,528 young women aged 15–24 years. Multivariate logistic regression was used to examine factors associated with the desired family size of young women. All analyses were conducted using Stata software version 17 and considered complex survey design. The prevalence of young women who had the desire of at least 4 children has been considerably high in Zambia, at 63.2%. Young women in the age group 20–24 were found to have higher odds (AOR = 1.31; 95% CI: 1.03, 1.66) of desiring at least 4 children compared to those aged 15–19. Women living in the rural areas were (AOR = 1.41; 95% CI: 1.10, 1.79) more likely to desire at least 4 children compared to their counterparts living in urban areas. Age of a young woman, place of residence, level of education, household wealth status, number of living children, and exposure to mass-media family planning messages were significantly associated with desire of at least 4 children. The desire for a large family size remains a social concern for reducing fertility in Zambia. This is because the proportion of young women who desire a large family size has been consistently high. Increasing access to education and sexual reproductive health information to young women especially to those in rural areas is key to changing their reproductive behaviour.

In this paper, two classes of large families of sequences of length pn-1 is proposed, where p is a prime number, n is an even number, n = 2m. One of them is binary, the new sequences have large family size 22n and seven-valued correlations, {-2m-1,-1,2m-1,2ldr2m-1,3ldr2m-1,4ldr2m -1,5 ldr2m -1}. The other is binary or ployphase, depending upon choice of the parameter p, the new sequences possess the large family size p(d-1)n, and at most 2d correlation levels, {-pm -1, -1,pm -1,2pm -1, ldrldrldr , (2d -2)pm -1}, where d is a positive integer such that d ges 2.1n addition, the later one includes the sequences with Niho-type decimations,2pm-1(called as Niho sequences for p = 2 and Helleseth sequences for p > 2,respectively) and 3 ldr2m-2, as special cases.

In this correspondence, we present a family of binary 2n sequences of period 2(2n-1) where n is an integer, which can be seen as a generalization of nonlinear binary sequences obtained from Z4 sequences and recently constructed GKW (Gold, Kasami, and Welch)-like sequences. The sequences have low correlations and are useful in code-division multiple-access (CDMA) communication systems and cryptography

A method for the synthesis of an infinite family of binary sequences with perfectly flat cross-correlation sidelobes is presented. The corresponding postprocessing arrays are similarly two-valued, and so the sequences may be particularly suited to applications in high noise environments.

Effects of primary and secondary morphological family size in monolingual and bilingual word processing

In earlier papers finite pseudorandom binary sequences were studied, quantitative measures of pseudorandomness of them were introduced and studied, and large families of “good” pseudorandom sequences were constructed. In certain applications (cryptography) it is not enough to know that a family of “good” pseudorandom binary sequences is large, it is a more important property if it has a “rich”, “complex” structure. Correspondingly, the notion of “f-complexity” of a family of binary sequences is introduced. It is shown that the family of “good” pseudorandom binary sequences constructed earlier is also of high f-complexity. Finally, the cardinality of the smallest family achieving a prescibed f-complexity and multiplicity is estimated.

Antibiotic resistance has been among the top public health threats elsewhere. Scientific information on knowledge, attitudes, and practices (KAP) at the community level towards antibiotic use and disposal ways is a vital step for effective intervention. This study aimed at determining the levels of KAP and associated risk factors for antibiotics in and around Hawassa City, southern Ethiopia. A community-based cross-sectional study was conducted, and data were collected using a structured questionnaire. Descriptive statistics, chi-square test, and logistic regression were used to analyze and interpret the results. A total of 504 participants with a mean age of 35.32 ± 9.03 years were included in the study. Most of the participants were urban dwellers (59.5%); more than half (55.6%) of the participants were male; most of the participants (62.7%) were at least college graduates; about half were employed (52.4%); about 41.7% of the participants had a large family size (≥7) with a mean family size of 5.7 ± 2.7; the average family monthly income was ETB 7213.71 ± 3673, and over three-fourth (74.8%) of the study participants were married. In addition, about 83.13% of the study participants heard about antibiotics; almost all of them (99.8%) had ever used antibiotics at some point in their life (75% of which used antibiotics within 6 months), and all of them could name at least one common type of antibiotic. Moreover, most of the participants (86.5%) did not receive any training related to antibiotics, and 29.4% of them obtained antibiotics without a prescription. Most participants had poor knowledge (64%), negative attitudes (60.4%), and poor practices (55%) towards antibiotic use, resistance, and disposal methods. Significant and positive linear correlations between knowledge and attitude (r = 0.539, P ≤ 0.001), knowledge-practice (r = 0.532, P ≤ 0.001), and attitude-practice (r = 0.786, P < 0.001) were also observed. Most of the sociodemographic variables were significantly associated with the mean KAP scores of the study participants. Living in a rural area, having a large family size, and being female, married, illiterate, and farmer resulted in a very low level of knowledge. Similarly, living in a rural area, having a small family size, and being older and married resulted in a negative attitude. Furthermore, having a smaller family size, having a low family monthly income, and being married, illiterate, and self-employed resulted in poor practice. A very low level of KAP towards antibiotics among people living in and around Hawassa City calls for urgent and effective intervention strategies.

In this paper, we construct two new families S and U of optimal quadriphase sequences. Compared to the family A constructed by Boztas et al and family D investigated by Tang et al respectively, the proposed families have the same optimal correlation properties and family size, but larger linear spans.

Spread spectrum multiple access systems demand minimum possible cross-correlation between the sequences within a set of sequences having good auto-correlation properties. Through a connection between generalised Frank sequences and Florentine arrays, we present a family of perfect sequences with low cross-correlation having a larger family size, compared with previous works. In particular, the family size can be equal to the square root of the period when the period of the perfect sequences is even. In contrast, the number of the perfect sequences of even period with low cross-correlation is equal to one in all previous works.