A class of cyclotomic linear codes and their generalized Hamming weights
نویسندگان
چکیده
منابع مشابه
A class of cyclotomic linear codes and their generalized Hamming weights
Abstract Firstly, we give a formula on the generalized Hamming weight of linear codes constructed generically by defining sets. Secondly, by choosing properly the defining set we obtain a class of cyclotomic linear codes and then present two alternative formulas to calculate their generalized Hamming weights. Lastly, we determine their weight distribution and generalized Hamming weights partial...
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In [22], Kelan Ding and Cunsheng Ding presented a class of linear codes and determined their weight distributions. In this paper, we focus on the generalized Hamming weights of these codes. In order to do so, we study the quadratic forms over subspaces of finite field and obtain some interesting results about subspaces and their dual spaces. On this basis, we solve all the generalized Hamming w...
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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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The generalized Hamming weights of a linear code have been extensively studied since Wei first use them to characterize the cryptography performance of a linear code over the wire-tap channel of type II. In this paper, we investigate the generalized Hamming weights of three classes of linear codes constructed through defining sets and determine them partly for some cases. Particularly, in the s...
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ژورنال
عنوان ژورنال: Applicable Algebra in Engineering, Communication and Computing
سال: 2018
ISSN: 0938-1279,1432-0622
DOI: 10.1007/s00200-018-0355-1