有限域上斜λ-常循环码中互补对偶码的存在性及其性质

doi:10.3976/j.issn.1002-4026.2019.03.013

Shandong Science ›› 2019, Vol. 32 ›› Issue (3): 85-89.doi: 10.3976/j.issn.1002-4026.2019.03.013

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Existence and properties of complementary-dual codes in skew λ-cyclic codes over finite fields

ZHAO Peng-cheng, LI Xiu-li^*

College of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China

Received:2018-08-12 Online:2019-06-20 Published:2019-06-01

Abstract

Abstract: Linear complementary-dual codes (LCD codes) have good correlation and orthogonal properties, which are one of the hot topics in coding theory research. In this paper, automorphism maps were introduced based on the ordinary polynomial ring, and the skew λ-cyclic codes over finite fields were obtained. We studied the existence and properties of the complementary-dual codes in the skew λ-cyclic codes over finite fields. Moreover, the counting problem of LCD codes in the skew λ-cyclic codes over finite fields was also discussed.

Key words: linear complementarity-dual codes, polynomial rings, automorphism mapping, skew λ-cyclic codes

CLC Number:

O236.2

ZHAO Peng-cheng, LI Xiu-li. Existence and properties of complementary-dual codes in skew λ-cyclic codes over finite fields[J].Shandong Science, 2019, 32(3): 85-89.

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Existence and properties of complementary-dual codes in skew λ-cyclic codes over finite fields

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