Five families of three-weight ternary cyclic codes and their duals

Cunsheng Ding; Ying Gao; Zhengchun Zhou

doi:10.1109/TIT.2013.2281205

Five families of three-weight ternary cyclic codes and their duals

Cunsheng Ding
, Ying Gao
, Zhengchun Zhou

School of Cyber Science and Technology

Hong Kong University of Science and Technology
Southwest Jiaotong University

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

As a subclass of linear codes, cyclic codes have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, five families of three-weight ternary cyclic codes whose duals have two zeros are presented. The weight distributions of the five families of cyclic codes are settled. The duals of two families of the cyclic codes are optimal.

Original language	English
Article number	6594807
Pages (from-to)	7940-7946
Number of pages	7
Journal	IEEE Transactions on Information Theory
Volume	59
Issue number	12
DOIs	https://doi.org/10.1109/TIT.2013.2281205
State	Published - Dec 2013

Keywords

Cyclic codes
frequency hopping sequences
secret sharing
weight distribution
weight enumerator

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10.1109/TIT.2013.2281205

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abstract = "As a subclass of linear codes, cyclic codes have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, five families of three-weight ternary cyclic codes whose duals have two zeros are presented. The weight distributions of the five families of cyclic codes are settled. The duals of two families of the cyclic codes are optimal.",

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AB - As a subclass of linear codes, cyclic codes have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, five families of three-weight ternary cyclic codes whose duals have two zeros are presented. The weight distributions of the five families of cyclic codes are settled. The duals of two families of the cyclic codes are optimal.

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KW - frequency hopping sequences

KW - secret sharing

KW - weight distribution

KW - weight enumerator

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Five families of three-weight ternary cyclic codes and their duals

Abstract

Keywords

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