Restrictions on the weight distribution of binary linear codes imposed by the structure of Reed-Muller codes
نویسنده
چکیده
Abstmcf-The words of a binary linear [n,k] code C whose weights belong to a given subset I C { 0, 1,. .. , n} constitute a word in a certain Reed-Muller code !R!Dl ((r, k). Appropriate choices of I result in low values of the order r and thus yield restrictions on the weight distribution of C.
منابع مشابه
Local Weight Distribution of the (256, 93) Third-Order Binary Reed-Muller Code
Local weight distribution is the weight distribution of minimal codewords in a linear code. We give the local weight distribution of the (256, 93) third-order binary Reed-Muller code. For the computation, a coset partitioning algorithm is modified by using a binary shift invariance property. This reduces the time complexity by about 1/256 for the code. A necessary and sufficient condition for m...
متن کاملOn the non-minimality of the largest weight codewords in the binary Reed-Muller codes
The study of minimal codewords in linear codes was motivated by Massey who described how minimal codewords of a linear code define access structures for secret sharing schemes. As a consequence of his article, Borissov, Manev, and Nikova initiated the study of minimal codewords in the binary Reed-Muller codes. They counted the number of non-minimal codewords of weight 2d in the binary Reed-Mull...
متن کاملOn Linear Codes over Z2s
In an earlier paper the authors studied simplex codes of type α and β over Z4 and obtained some known binary linear and nonlinear codes as Gray images of these codes. In this correspondence, we study weight distributions of simplex codes of type α and β over Z2s . The generalized Gray map is then used to construct binary codes. The linear codes meet the Griesmer bound and a few non-linear codes...
متن کاملOn the Stabilizer of Weight Enumerators of Linear Codes
This paper investigates the relation between linear codes and the stabilizer in GL2(C) of their weight enumerators. We prove a result on the finiteness of stabilizers and give a complete classification of linear codes with infinite stabilizer in the non-binary case. We present an efficient algorithm to compute explicitly the stabilizer of weight enumerators and we apply it to the family of Reed...
متن کاملAnother Generalization of the Reed-Muller Codes
The punctured binary Reed-Muller code is cyclic and was generalized into the punctured generalized ReedMuller code over GF(q) in the literature. The major objective of this paper is to present another generalization of the punctured binary Reed-Muller code. Another objective is to construct a family of reversible cyclic codes that are related to the newly generalized Reed-Muller codes. Index Te...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- IEEE Trans. Information Theory
دوره 40 شماره
صفحات -
تاریخ انتشار 1994