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Hamming weights in irreducible cyclic codes. (English) Zbl 1269.94040

In this paper, the authors give a survey of earlier results on the weight distributions of irreducible cyclic codes and obtain some extensions and generalizations of these earlier results. They give a complete characterization of one-weight irreducible cyclic codes (that extends an earlier result obtained by G. Vega and J. Wolfmann [Des. Codes Cryptography 42, No. 3, 327–334 (2007; Zbl 1132.94011)]. Some examples for weight distributions of one-, two-, three-, and four-weight codes over different fields are given. Also, the authors obtain a lower and upper bound of irreducible cyclic codes.

MSC:

94B15 Cyclic codes
05B10 Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)
11T22 Cyclotomy
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
94B65 Bounds on codes

Citations:

Zbl 1132.94011
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