The symbol-pair distance distribution of repeated-root cyclic codes over ${\mathbb{F}}_{p^m}$

Abstract

Symbol-pair codes are proposed to protect against pair errors in symbol-pair read channels. One of the most important task in symbol-pair coding theory is to determine the minimum pair-distance of symbol-pair codes. In this paper, we investigate the symbol-pair distances of cyclic codes of length $p^e$ over ${\mathbb{F}}_{p^m}$. The exact symbol-pair distances of all cyclic codes of such length are determined.