Generalized Hamming Weights for Almost Affine Codes
نویسندگان
چکیده
منابع مشابه
Generalized Hamming weights for linear codes
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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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...
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Coset constructions of q-ary Reed-Muller codes can be used to store secrets on a distributed storage system in such a way that only parties with access to a large part of the system can obtain information while still allowing for local error-correction. In this paper we determine the relative generalized Hamming weights of these codes which can be translated into a detailed description of the i...
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Motivated by applications in cryptology, Wei (1991) introduced the concept of a generalized Hamming weight for a linear block code. In this correspondence, we define generalized Hamming weights for the class of convolutional codes and we derive several of their basic properties. By restricting to convolutional codes having a generator matrix G(D) with bounded Kronecker indices we are able to de...
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The order bound on generalized Hamming weights is introduced in a general setting of codes on varieties which comprises both the one point geometric Goppa codes as the q-ary Reed-Muller codes. For the latter codes it is shown that this bound is sharp and that they satisfy the double chain condition.
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2017
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2017.2654456