Intersection of isomorphic linear codes

[摘要] Given an (n, k) linear code C over GF(q), the intersection of C with a code n(C), where pi is an element of S-n, is an (n, k(1)) code, where max{0, 2k - n} less than or equal to k(1) less than or equal to 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. (C) 1997 Academic Press.

[发布日期] 1997-11-01