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 کاملRelative generalized Hamming weights of cyclic codes
Abstract. Relative generalized Hamming weights (RGHWs) of a linear code respect to a linear subcode determine the security of the linear ramp secret sharing scheme based on the code. They can be used to express the information leakage of the secret when some keepers of shares are corrupted. Cyclic codes are an interesting type of linear codes and have wide applications in communication and stor...
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 کاملOn Binary Cyclic Codes with Five Nonzero Weights
Let q = 2, 0 ≤ k ≤ n − 1, n/ gcd(n, k) be odd and k 6= n/3, 2n/3. In this paper the value distribution of following exponential sums
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ژورنال
عنوان ژورنال: Information and Control
سال: 1977
ISSN: 0019-9958
DOI: 10.1016/s0019-9958(77)80009-0