931 research outputs found
On the complete weight enumerators of some linear codes with a few weights
Linear codes with a few weights have important applications in authentication
codes, secret sharing, consumer electronics, etc.. The determination of the
parameters such as Hamming weight distributions and complete weight enumerators
of linear codes are important research topics. In this paper, we consider some
classes of linear codes with a few weights and determine the complete weight
enumerators from which the corresponding Hamming weight distributions are
derived with help of some sums involving Legendre symbol
Self-Dual Codes
Self-dual codes are important because many of the best codes known are of
this type and they have a rich mathematical theory. Topics covered in this
survey include codes over F_2, F_3, F_4, F_q, Z_4, Z_m, shadow codes, weight
enumerators, Gleason-Pierce theorem, invariant theory, Gleason theorems,
bounds, mass formulae, enumeration, extremal codes, open problems. There is a
comprehensive bibliography.Comment: 136 page
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