On the Symbol-Pair Distance of Repeated-Root Constacyclic Codes of Prime Power Lengths
Hai Quang Dinh, Bac Trong Nguyen, Abhay Kumar Singh, Songsak Sriboonchitta · IEEE Transactions on Information Theory · 2017
Let p be a prime, and λ be a nonzero element of the finite field Fpm. The λ-constacyclic codes of length psover Fpmare linearly ordered under set-theoretic inclusion, i.e., they are the ideals 〈(x - λ0)i〉, 0 ≤ i ≤ psof the chain ring [(Fpm[x])/((xps- λ))]. This structure is used to establish the symbol-pair distances of all such λ-constacyclic codes. Among others, all maximum distance separable symbol-pair constacyclic codes of length ps are obtained.