منابع مشابه
On Minimal and Almost-Minimal Linear Codes
Minimal linear codes are such that the support of every codeword does not contain the support of another linearly independent codeword. Such codes have applications in cryptography, e.g. to secret sharing and secure two-party computations. We pursue here the study of minimal codes and construct infinite families with asymptotically non-zero rates. We also introduce a relaxation to almost minima...
متن کاملVariations on Minimal Linear Codes
Minimal linear codes are linear codes such that the support of every codeword does not contain the support of another linearly independent codeword. Such codes have applications in cryptography, e.g. to secret sharing. We pursue here their study and construct asymptotically good families of minimal linear codes. We also push further the study of quasi-minimal and almost-minimal linear codes, re...
متن کاملBounds on Minimal Codewords in Linear Codes
The notion of minimal codewords in linear codes was introduced recently by Massey. In this paper two weight bounds on minimal code-words are proved; an upper bound above which no codewords are minimal and a lower bound below which all codewords are minimal. It is shown for Hamming codes that every weight class between the two bounds contains at least one minimal codeword and at least one non-mi...
متن کاملLinear Codes With Two or Three Weights From Some Functions With Low Walsh Spectrum in Odd Characteristic
Linear codes with few weights have applications in authentication codes, secrete sharing schemes, association schemes, consumer electronics and data storage system. In this paper, several classes of linear codes with two or three weights are obtained from some functions with low Walsh spectrum in odd characteristic. Numerical results show that some of the linear codes obtained are optimal or al...
متن کاملMinimal Linear Codes over Finite Fields
As a special class of linear codes, minimal linear codes have important applications in secret sharing and secure two-party computation. Constructing minimal linear codes with new and desirable parameters has been an interesting research topic in coding theory and cryptography. Ashikhmin and Barg showed that wmin/wmax > (q− 1)/q is a sufficient condition for a linear code over the finite field ...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2019
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2019.2891992