منابع مشابه
Computation of Minimum Hamming Weight for Linear Codes
In this paper, we consider the minimum Hamming weight for linear codes over special finite quasi-Frobenius rings. Furthermore, we obtain minimal free $R$-submodules of a finite quasi-Frobenius ring $R$ which contain a linear code and derive the relation between their minimum Hamming weights. Finally, we suggest an algorithm that computes this weight using the Grobner basis and we show that und...
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We derive a recursive formula determining the weight distribution of the [n = (qm − 1)/(q − 1), n − m, 3] Hamming code H(m, q), when (m, q−1) = 1. Here q is a prime power. The proof is based on Moisio’s idea of using Pless power moment identity together with exponential sum techniques.
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Jung-Fu Cheng Robert J. McEliece WWW Address: http://www.cco.caltech.edu/~rjm/ California Institute of Technology 116-81, Pasadena, CA 91125, USA (Draft of September 11, 1995)
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We consider a code to be a subset of the vertex set of a Hamming graph. We examine elusive pairs, code-group pairs where the code is not determined by knowledge of its set of neighbours. We construct a new infinite family of elusive pairs, where the group in question acts transitively on the set of neighbours of the code. In our examples, we find that the alphabet size always divides the length...
متن کاملHamming codes and some theory of linear error correcting codes
The topic is how to reduce the error of communication in the presence of noise. Block encoding is an expansion function from a block of plaintext alphabet symbols to a block of communication alphabet symbols where the block lengths are k and n respectively, and k ≤ n. Without loss of generality we consider both alphabets to be bit strings. The notation for an i length bit string is σ ∈ { 0, 1 }...
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ژورنال
عنوان ژورنال: Electronics and Control Systems
سال: 2010
ISSN: 1990-5548
DOI: 10.18372/1990-5548.23.759