منابع مشابه
On The Weights of Irreducible Cyclic Codes
The paper is devoted to the study of the weight distribution of irreducible cyclic codes. We start from the interpretation due to McEliece of these weights by means of Gauss sums. Firstly, a p-adic analysis using Stickelberger congruences and Gross-Koblitz formula enable us to improve the divisibility theorem of McEliece by giving results on the multiplicity of the weights. Secondly, in connect...
متن کاملHamming weights in irreducible cyclic codes
The objectives of this paper are to survey and extend earlier results on the weight distributions of irreducible cyclic codes, present a divisibility theorem and develop bounds on the weights in irreducible cyclic codes. © 2012 Elsevier B.V. All rights reserved.
متن کاملOn the Weights of Binary Irreducible Cyclic Codes
This paper is devoted to the study of the weights of binary irreducible cyclic codes. We start from McEliece’s interpretation of these weights by means of Gauss sums. Firstly, a dyadic analysis, using the Stickelberger congruences and the Gross-Koblitz formula, enables us to improve McEliece’s divisibility theorem by giving results on the multiplicity of the weights. Secondly, in connection wit...
متن کاملGood Quasi-Cyclic Codes Derived From Irreducible Cyclic Codes
As a generalization of cyclic codes, quasi-cyclic codes contain many good linear codes. Extensive search is made and lots of good quasi-cyclic codes are obtained from irreducible cyclic codes. A new binary [95, 13, 40] code which improves the lower bound on the minimum distance, is also constructed. Index Term — Codes and coding, linear codes, cyclic codes, idempotent, irreducible codes, quasi-...
متن کاملWeight enumerator of some irreducible cyclic codes
In this article, we show explicitly all possible weight enumerators for every irreducible cyclic code of length n over a finite field Fq, in the case which each prime divisor of n is also a divisor of q − 1.
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ژورنال
عنوان ژورنال: Information and Control
سال: 1972
ISSN: 0019-9958
DOI: 10.1016/s0019-9958(72)90354-3