A family of optimal ternary cyclic codes with minimum distance five and their duals

Wang, Dandan; Cao, Xiwang

doi:10.1007/s12095-021-00493-z

Cited by 5 publications

(1 citation statement)

References 26 publications

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“…Ding and Helleseth [7] constructed several classes of optimal ternary cyclic codes C (1,e) with parameters [3 m − 1, 3 m − 1 − 2m, 4] by using almost perfect nonlinear monomials and some other monomials over F 3 m . Subsequently, many classes of optimal ternary cyclic codes C (1,e) with parameters [3 m − 1, 3 m − 1 − 2m, 4] were constructed successively [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Two Classes of Optimal Ternary Cyclic Codes with Minimum Distance Four

HE,

RAN,

LUO

2024

IEICE Trans. Fundamentals

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This article has been accepted and published on J-STAGE in advance of copyediting. Content is final as presented. LETTER Two classes of optimal ternary cyclic codes with minimum distance fourChao HE † * a) , Xiaoqiong RAN † * b) , Nonmembers, and Rong LUO † * c) , Member SUMMARYCyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. Let C (t,e) denote the cyclic code with two nonzero α t and α e , where α is a generator of F * 3 m . In this letter, we investigate the ternary cyclic codes with parameters [3 m −1, 3 m −1−2m, 4] based on some results proposed by Ding and Helleseth in 2013. Two new classes of optimal ternary cyclic codes C (t,e) are presented by choosing the proper t and e and determining the solutions of certain equations over F 3 m .

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