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On the Hamming distances of repeated-root constacyclic codes of length 4ps


Hai Q. Dinh, Xiaoqiang Wang, Hongwei Liu, Songsak Sriboonchitta

Source title: 
Discrete Mathematics, 342(5): 1456-1470, 2019 (ISI)
Academic year of acceptance: 

Let 4_QungHai.png be an odd prime, 5_QuangHai.png be positive integers, 6_QuangHai.png be nonzero elements of the finite field 7_QuangHai.png such that 8_QuangHai.png. In this paper, we show that, for any positive integer 9_QuangHai.png, the Hamming distances of all repeated-root 10_QuangHai.pngconstacyclic codes of length 11_QuangHai.png can be determined by those of certain simple-root 12_QuangHai.pngconstacyclic codes of length 9_QuangHai.png. Using this result, Hamming distances of all constacyclic codes of length 13_QuangHai.png are obtained. As an application, we identify all MDS 10_QuangHai.pngconstacyclic codes of length 13_QuangHai.png.