Construction and decoding of BCH codes over finite commutative rings

BCH codes over arbitrary finite commutative rings with identity are derived in terms of their locator vector. The derivation is based on the factorization of xs -1 over the unit ring of an appropriate extension of the finite ring. We present an efficient decoding procedure, based on the modified Berlekamp-Massey algorithm, for these codes. The code construction and the decoding procedures are very similar to the BCH codes over finite integer rings. © 1999 Elsevier B.V. All rights reserved.

A decoding method of an n length binary BCH code through (n + 1)n length binary cyclic code

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Caracterização das habilidades do processamento auditivo em crianças com desnutrição

Pós-graduação em Fonoaudiologia - FFC

Para além da leitura linear: uma contribuição ao processo de compreensão

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Construction and decoding of BCH codes over chain of commutative rings

In this paper, we present a new construction and decoding of BCH codes over certain rings. Thus, for a nonnegative integer t, let A0 ⊂ A1 ⊂···⊂ At−1 ⊂ At be a chain of unitary commutative rings, where each Ai is constructed by the direct product of appropriate Galois rings, and its projection to the fields is K0 ⊂ K1 ⊂···⊂ Kt−1 ⊂ Kt (another chain of unitary commutative rings), where each Ki is made by the direct product of corresponding residue fields of given Galois rings. Also, A∗ i and K∗ i are the groups of units of Ai and Ki, respectively. This correspondence presents a construction technique of generator polynomials of the sequence of Bose, Chaudhuri, and Hocquenghem (BCH) codes possessing entries from A∗ i and K∗ i for each i, where 0 ≤ i ≤ t. By the construction of BCH codes, we are confined to get the best code rate and error correction capability; however, the proposed contribution offers a choice to opt a worthy BCH code concerning code rate and error correction capability. In the second phase, we extend the modified Berlekamp-Massey algorithm for the above chains of unitary commutative local rings in such a way that the error will be corrected of the sequences of codewords from the sequences of BCH codes at once. This process is not much different than the original one, but it deals a sequence of codewords from the sequence of codes over the chain of Galois rings.

Goppa codes through polynomials of B[X;(1/2^2)Z_0] and its decoding principle

In this paper, we present a decoding principle for Goppa codes constructed by generalized polynomials, which is based on modified Berlekamp-Massey algorithm. This algorithm corrects all errors up to the Hamming weight $t\leq 2r$, i.e., whose minimum Hamming distance is $2^{2}r+1$.

A decoding procedure which improves code rate and error corrections

Corresponding to $C_{0}[n,n-r]$, a binary cyclic code generated by a primitive irreducible polynomial $p(X)\in \mathbb{F}_{2}[X]$ of degree $r=2b$, where $b\in \mathbb{Z}^{+}$, we can constitute a binary cyclic code $C[(n+1)^{3^{k}}-1,(n+1)^{3^{k}}-1-3^{k}r]$, which is generated by primitive irreducible generalized polynomial $p(X^{\frac{1}{3^{k}}})\in \mathbb{F}_{2}[X;\frac{1}{3^{k}}\mathbb{Z}_{0}]$ with degree $3^{k}r$, where $k\in \mathbb{Z}^{+}$. This new code $C$ improves the code rate and has error corrections capability higher than $C_{0}$. The purpose of this study is to establish a decoding procedure for $C_{0}$ by using $C$ in such a way that one can obtain an improved code rate and error-correcting capabilities for $C_{0}$.

A comunicação não verbal da equipe de enfermagem contribuindo para o cuidado do idoso em internação hospitalar

Pós-graduação em Enfermagem (mestrado profissional) - FMB

Minas e a aclamação de D. João VI no limiar da formação do Estado-Nação brasileiro: memórias, conflitos e sedições

Dans cet article on examinera les cérémonies d'acclamation du roi D. João VI qui ont eu lieu à Tejuco en 1818. Le décodage de la riche variété d'images esthétiques présente dans ces célébrations peut être une stratégie privilégiée pour comprendre la création, à ce moment-là, des mythes qui donneraient soutien et orientation au projet d'affirmation du prestige politique du roi et à la consolidation de sa domination sur la région et sur tout le territoire brésilien. on analysera en particulier le conflit de mémoires entre la signification symbolique de la célébration et la révolte du peuple de Minas contre l'exploitation coloniale portugaise qui avait éclaté dans la région environ trois décennies avant.

Contato corporal entre adolescentes através da dança de salão na escola

The objective of this study was to identify the reaction and perception of adolescents in relation to body contact as well as emotional expressions through ballroom dancing. Forty-two adolescents from a public elementary school in the state of São Paulo participated in the study. Data gathering was conducted in groups by filming the ballroom dance class and applying a questionnaire about the experience. The dance experience was observed to provide greater body proximity and demonstration of affection, since part of the participants reported well-being, while others reported being embarrassed by dancing with a partner from the opposite sex. It was concluded that more dance activities related to biopsychosocial development need to be offered at school since ballroom dancing can help in interaction promoting body contact and thus facilitate in the process of interpersonal relations between adolescents.

Introdução da comunicação suplementar e alternativa na terapia com afásicos

Sabe-se que o tratamento fonoaudiológico de pacientes com afasia severa é limitado. A ausência de fala articulada, algumas vezes, impede o diagnóstico da afasia. O paciente grave pode não falar devido à inabilidade de articulação, como ocorre na disartria e/ou apraxia. Essa ausência de fala não permite afirmar se a linguagem está comprometida. O uso da comunicação suplementar e alternativa tem sido um método eficaz na reabilitação desses pacientes. Esse estudo visou descrever o uso da comunicação suplementar e alternativa associada a outras modalidades de linguagem (escrita, gestos), a partir do relato de dois casos de afasia. A análise dos dados foi composta por dois blocos: a introdução da comunicação suplementar e alternativa no diálogo; e o uso da leitura e escrita associado aos símbolos. A comunicação suplementar e alternativa foi um apoio para a oralidade, leitura e escrita dos pacientes.

Habilidades expressivas de um grupo de alunos com paralisia cerebral na atividade de jogo

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)