Generalized Hamming Weights of Irreducible Cyclic Codes

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Hamming 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.

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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...

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Error control codes are widely used to increase the reliability of transmission of information over various forms of communications channels. The Hamming weight of a codeword is the number of nonzero entries in the word; the weights of the words in a linear code determine the error-correcting capacity of the code. The rth generalized Hamming weight for a linear code C, denoted by dr(C), is the ...

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ژورنال

عنوان ژورنال: IEEE Transactions on Information Theory

سال: 2015

ISSN: 0018-9448,1557-9654

DOI: 10.1109/tit.2015.2444013