Intersection of Isomorphic Linear Codes

✍ Scribed by Eli Bar-Yahalom; Tuvi Etzion

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 308 KB
• Volume: 80
• Category: Article
• ISSN: 0097-3165
• DOI: 10.1006/jcta.1997.2805

✦ Synopsis

Given an (n, k) linear code C over GF(q), the intersection of C with a code ?(C), where ? # S n , is an (n, k 1 ) code, where max[0, 2k&n] k 1 k. The intersection problem is to determine which integers in this range are attainable for a given code C. We show that, depending on the structure of the generator matrix of the code, some of the values in this range are attainable. As a consequence we give a complete solution to the intersection problem for most of the interesting linear codes, e.g. cyclic codes, Reed Muller codes, and most MDS codes.