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

TL;DR

This paper determines the exact symbol-pair distances of all cyclic codes of length p^e over finite fields, advancing the understanding of error correction in symbol-pair read channels.

Contribution

It provides a complete characterization of the symbol-pair distances for cyclic codes of length p^e over finite fields, filling a key gap in coding theory.

Findings

Exact symbol-pair distances for all cyclic codes of length p^e over _{p^m}

Enhanced understanding of error correction capabilities in symbol-pair channels

Foundation for designing more robust symbol-pair codes

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.