Computer Science – Information Theory
Scientific paper
2012-03-07
Computer Science
Information Theory
29 pages, 1 Table, 1 Appendix, revised on 3/25/2012
Scientific paper
Binary optimal codes often contain optimal or near-optimal subcodes. In this paper we show that this is true for many optimal codes including self-dual codes and formally self-dual codes. One approach is to compute the optimum distance profiles (ODPs) of linear codes, which was introduced by Luo, et. al. (2010) due to the practical applications to WCDMA and address retrieval on optical media. One of our main results is the development of general algorithms, called the Chain Algorithms, for finding ODPs of linear codes. Then we determine the ODPs for the Type II codes of lengths up to 24 and the extremal Type II codes of length 32, give a partial result of the ODP of the extended quadratic residue code $q_{48}$ of length 48, and determine the ODPs of optimal formally self-dual codes with parameters $[16, 8, 5], [18, 9, 6], [20, 10, 6]$ and $[22,11,7]$. We also show that there does not exist a $[48,k,16]$ subcode of $q_{48}$ for $k \ge 17$, and we find a first example of a {\em doubly-even} self-complementary $[48, 16, 16]$ code.
Freibert Finley
Kim Jon-Lark
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