Matrix characterization of linear codes with arbitrary Hamming weight hierarchy
نویسندگان
چکیده
منابع مشابه
Matrix characterization of linear codes with arbitrary Hamming weight hierarchy
The support of an [n, k] linear code C over a finite field Fq is the set of all coordinate positions such that at least one codeword has a nonzero entry in each of these coordinate position. The rth generalized Hamming weight dr (C), 1 r k, of C is defined as the minimum of the cardinalities of the supports of all [n, r] subcodes of C. The sequence (d1(C), d2(C), . . . , dk(C)) is called the Ha...
متن کاملComputation 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...
متن کاملWeight Distributions of Hamming Codes
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.
متن کاملWeight Distributions of Hamming Codes (II)
In a previous paper, we derived a recursive formula determining the weight distributions 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. We note here that the formula actually holds for any positive integer m and any prime power q, without the restriction (m,q − 1) = 1.
متن کاملThe weight hierarchy of a family of cyclic codes with arbitrary number of nonzeroes
The generalized Hamming weights (GHWs) are fundamental parameters of linear codes. GHWs are of great interest in many applications since they convey detailed information of linear codes. In this paper, we continue the work of [10] to study the GHWs of a family of cyclic codes with arbitrary number of nonzeroes. The weight hierarchy is determined by employing a number-theoretic approach.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2006
ISSN: 0024-3795
DOI: 10.1016/j.laa.2005.07.008