Title :
Polyadic Constacyclic Codes
Author :
Bocong Chen ; Dinh, Hai Q. ; Yun Fan ; San Ling
Author_Institution :
Sch. of Phys. & Math. Sci., Nanyang Technol. Univ., Singapore, Singapore
Abstract :
For any given positive integer m, a necessary and sufficient condition for the existence of Type-I m-adic constacyclic codes is given. Furthermore, for any given integer s, a necessary and sufficient condition for s to be a multiplier of a Type-I polyadic constacyclic code is given. As an application, some optimal codes from Type-I polyadic constacyclic codes, including generalized Reed-Solomon codes and alternant maximum distance separable codes, are constructed.
Keywords :
Reed-Solomon codes; cyclic codes; decoding; Berlekamp-Welch decoding algorithm; alternant maximum distance separable codes; generalized Reed-Solomon codes; optimal codes; polyadic constacyclic codes; type-I m-adic constacyclic codes; Cost accounting; Decoding; Electronic mail; Indexes; Polynomials; Reed-Solomon codes; Zirconium; $p$ -adic valuation; Berlekamp- Welch decoding algorithm.; Berlekamp-Welch decoding algorithm; Polyadic constacyclic code; alternant code; generalized Reed-Solomon code;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2015.2451656
