On Distances of Family of Constacyclic Codes over Finite Chain Rings
YUAN Jian ZHU Shixin KAI Xiaoshan
(School of Mathematics, Hefei University of Technology, Hefei 230009, China)
(National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China)
In coding theory, the (minimum) distance of a code is a very important invariant, which always determines the error-correcting capability of the code. Let R be an arbitrary commutative finite chain ring, a is a generator of the unique maximal ideal and R* is the multiplicative group of units of R. In this paper, for any w∈R*, by using the generator polynomials of (1+aw)-constacyclic codes of any length over R, higher torsion codes of such codes are calculated. The Hamming distance of all (1+aw)-constacyclic codes of any length over R is determined and the exact homogeneous distance of some such codes is obtained. The result provides a theoretical basis for encoding and decoding for such constacyclic codes.
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YUAN Jian, ZHU Shixin, KAI Xiaoshan. On Distances of Family of Constacyclic Codes over Finite Chain Rings. JEIT, 2017, 39(3): 754-757.
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