Ding, Cunsheng; Yang, Jing Hamming weights in irreducible cyclic codes. (English) Zbl 1269.94040 Discrete Math. 313, No. 4, 434-446 (2013). 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. Reviewer: Zlatko Varbanov (Veliko Tarnovo) Cited in 1 ReviewCited in 111 Documents 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 Keywords:cyclic codes; difference sets; weight distribution; Gaussian periods; cyclotomy Citations:Zbl 1132.94011 PDFBibTeX XMLCite \textit{C. Ding} and \textit{J. Yang}, Discrete Math. 313, No. 4, 434--446 (2013; Zbl 1269.94040) Full Text: DOI arXiv