Binary linear codes from vectorial boolean functions and their weight distribution
نویسندگان
چکیده
منابع مشابه
Binary linear codes from vectorial boolean functions and their weight distribution
Binary linear codes with good parameters have important applications in secret sharing schemes, authentication codes, association schemes, and consumer electronics and communications. In this paper, we construct several classes of binary linear codes from vectorial Boolean functions and determine their parameters, by further studying a generic construction developed by Ding et al. recently. Fir...
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Boolean functions have important applications in cryptography and coding theory. Two famous classes of binary codes derived from Boolean functions are the Reed-Muller codes and Kerdock codes. In the past two decades, a lot of progress on the study of applications of Boolean functions in coding theory has been made. Two generic constructions of binary linear codes with Boolean functions have bee...
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Let V be a binary linear (n,k)-code defined by a check matrixHwithcohmmsh,,~~~,h,,,andleth(x)=l ifxE(h,;..,h,),and h(x)=0 if x@{h,;.. ,h,}. A combinatorial argument relates the Walsh transform of h(x) with the weight distribution A(i) of the code V for small i(i< 7). This leads to another proof of the Pless ith power moment identities for i < 7. This relation also provides a simple method for c...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2017
ISSN: 0012-365X
DOI: 10.1016/j.disc.2017.07.008