We introduce the Hamming ball sampler, a novel Markov chain Monte Carlo algorithm, for efficient inference in statistical models involving high-dimensional discrete state spaces. The sampling scheme uses an auxiliary variable construction that adaptively truncates the model space allowing iterative exploration of the full model space. The approach generalizes conventional Gibbs sampling schemes...

It is desirable to study upper and lower bounds on the minimum distance and dimensions of quantum codes, so the computer search on the code parameter can be minimized and optimal codes can be known. It is a well-known fact that Singleton and Hamming bounds hold for classical codes [9]. We need some bounds on the achievable minimum distance of a quantum stabilizer code. Perhaps the simplest one ...

Given Hamming coded or systematic Bose–Chaudhuri-Hocquenghem (BCH) or Reed-Solomon correctable operands x and y and an operation op , we present arithmetic to compute the operation Correct( x )opCorrect(y) while preserving the correct-ability of the result. If the Hamming distance of x(y) from Correct(x) (Correct(y)) is dx (dy, respectively) and the maximal correctable distance is dc then our i...

Baseado nas referências apresentadas, o presente artigo aborda conceitos básicos para a construção de códigos corretores erros. Esses são utilizados aumentar confiabilidade da informação durante armazenamento e/ou transmissão dados. Abordamos também os lineares, que formam uma classe especial erros fáceis descrever graças sua estrutura algébrica. Além disso, descritos Hamming. Essa família foi ...

A finite ring R and a weight w on R satisfy the Extension Property if every R linear w -isometry between two R -linear codes in R extends to a monomial transformation of R n that preserves w . MacWilliams proved that finite fields with the Hamming weight satisfy the Extension Property. It is known that finite Frobenius rings with either the Hamming weight or the homogeneous weight satisfy the E...