A Construction of Binary Punctured Linear Codes and A Supporting Method for Best Code Search

Abstract

Reduction of redundancy and improvement of error-correcting capability are essential research themes in the coding theory. The best codes constructed in various ways are recorded in a database maintained by Markus Grassl. In this paper, we propose an algorithm to construct the best code using punctured codes and a supporting method for constructing the best codes. First, we define a new evaluation function to determine deletion bits and propose an algorithm for constructing punctured linear codes. 36 best codes were constructed in the proposed algorithm, and 131 best codes were constructed by further modifying those best codes. Secondly, we evaluate the possibility of increasing the minimum distance based on the relationship between code length, information length, and minimum distance. We narrowed down the target (n,k) code to try the best code search based on the evaluation and found 30 other best codes.