AntiGriesmer Bounds, Optimal Codes, and Their Subcode Support Weight Distributions

Seven infinite classes of relative difference families with variable block sizes are presented explicitly. In particular, a balanced (gv,g,K,1)-DF with g=Σk∈K[(k2-k)/2] is explicitly given for: (i) K={3,4,5} and every v coprime to 6; (ii) K={3,4,6}, {3,5,6} or {3,4,5,6} and every v coprime to 30. As far as the authors are aware, these difference families can be viewed as the first explicit constructions of infinite classes of optimal variable-weight optical orthogonal codes with more than two weights. It is observed, however, that there are infinitely many values of v for which an optimal (v,W,1,Q) -OOC exists, whatever the set of weights W and the weight distribution sequence Q are.

O objetivo deste trabalho foi padronizar e testar o uso da plataforma de força em padrão ortostático em cães, na avaliação do apoio e distribuição do peso nos membros, permitindo visualizar uma possível transferência em pacientes ortopédicos com afecções articulares. Foram realizadas avaliações clínica - graus de claudicação e exame radiográfico - e biomecânica na plataforma de força, por coleta estática de 16 pacientes cirúrgicos ortopédicos com afecções coxofemoral da rotina hospitalar (grupo tratado), e de seis cães saudáveis, sem histórico de problemas ortopédicos (grupo-controle). Com base no grupo-controle, foi possível delinear uma metodologia adequada para cães em coleta estática e testá-la no grupo tratado. A plataforma em padrão ortostático mostrou ser um parâmetro objetivo, eficiente e mais sensível que os demais, sendo seu uso adequado na avaliação de pacientes ortopédicos.

In this paper, we study the decoding error probability of linear codes over the erasure channel under the list decoding. The notion of the $q^\ell $ -incorrigible sets of linear codes is introduced to characterize its decoding error probability under the list decoding or the maximum likelihood decoding. By calculating the $q^\ell $ -incorrigible set distributions, the decoding error probability of a linear code over the erasure channel under the list decoding or the maximum likelihood decoding is expressed by its support weight distributions. For the ensemble of all $[n,k]$ linear codes, the average decoding error probability under the maximum likelihood decoding and the average unsuccessful decoding probability under unambiguous decoding are determined. Furthermore, the error exponent of the average unsuccessful decoding probability under the unambiguous decoding is determined for the ensemble of all $[n,nR]$ linear codes.

The support weight distribution of a code is the number of unique subspaces of the code with specified dimension and support weight. In this paper, we formulate the average second support weight distribution and its asymptotic exponent of regular LDPC code ensembles

In this correspondence, the generalized MacWilliams identities between the support weight distributions of a /spl Zopf//sub 4/-linear code of type 4/sup k/ and that of its dual are established.