Efficient Algorithms for Searching Optimal Shortened Cyclic Single-Burst-Correcting Codes

TL;DR

This paper introduces an efficient algorithm to identify optimal shortened cyclic burst-correcting codes, providing improved or matching constructions for burst lengths up to 10, enhancing coding efficiency.

Contribution

The paper presents a novel algorithm for searching optimal shortened cyclic burst-correcting codes, advancing code construction methods for burst lengths up to 10.

Findings

Generated extensive tables of codes that match or improve existing constructions.

Demonstrated the algorithm's effectiveness in finding optimal codes for burst lengths up to 10.

Confirmed the importance of the Gallager bound for code efficiency evaluation.

Abstract

In a previous work it was shown that the best measure for the efficiency of a single burst-correcting code is obtained using the Gallager bound as opposed to the Reiger bound. In this paper, an efficient algorithm that searches for the best (shortened) cyclic burst-correcting codes is presented. Using this algorithm, extensive tables that either tie existing constructions or improve them are obtained for burst lengths up to b=10.