Title :
Five Families of Three-Weight Ternary Cyclic Codes and Their Duals
Author :
Cunsheng Ding ; Ying Gao ; Zhengchun Zhou
Author_Institution :
Dept. of Comput. Sci. & Eng., Hong Kong Univ. of Sci. & Technol., Kowloon, China
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.
Keywords :
cyclic codes; dual codes; linear codes; ternary codes; communication system; consumer electronics; data storage system; decoding algorithm; dual code; encoding algorithm; linear code; ternary cyclic code; weight distribution; Cryptography; Educational institutions; Generators; Hamming weight; Linear code; Polynomials; Cyclic codes; frequency hopping sequences; secret sharing; weight distribution; weight enumerator;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2013.2281205
