On decoding procedures of intertwining codes

Abstract

The barrier of the family of centralizer codes is the length which is always n². In our paper, we have taken codes generated by two matrices A and C of different orders n × n and k × k respectively. This family of codes are termed as intertwining codes and denoted by . Specialty of this code is the length nk which gives a new approach to characterize family of centralizer codes. In this article, we show an upper bound on the minimum distance of intertwining codes. Besides, we establish two decoding methods which can be fitted to intertwining codes as well as for any linear codes. Moreover, we have shown a condition for which a linear code can be represented as an intertwining code.

Subject Classification:

• 94B05
• 94B35
• 15A24

Keywords:

• Linear codes
• Centralizer codes
• Syndrome decoding