On self-dual, doubly even codes of length 32
Journal of Combinatorial Theory Series A
Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes
Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes
Introduction to Coding Theory
On Repeated-Root Cyclic Codes and the Two-Way Chain Condition
AAECC-12 Proceedings of the 12th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Geometric approach to higher weights
IEEE Transactions on Information Theory - Part 1
On binary linear codes which satisfy the two-way chain condition
IEEE Transactions on Information Theory
Trellis decoding complexity of linear block codes
IEEE Transactions on Information Theory - Part 1
The twisted squaring construction, trellis complexity, and generalized weights of BCH and QR codes
IEEE Transactions on Information Theory - Part 1
On the intractability of permuting a block code to minimize trellis complexity
IEEE Transactions on Information Theory - Part 1
Self-dual codes over and of length not exceeding 16
IEEE Transactions on Information Theory
Support Weight Enumerators and Coset Weight Distributions of Isodual Codes
Designs, Codes and Cryptography
Second support weights for binary self-dual codes
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
| Hi-index | 0.00 |
A method for demonstrating and enumerating uniformly efficient (permutation-optimal) trellis decoders for self-dual codes of high minimum distance is developed. Such decoders and corresponding permutations are known for relatively few codes.The task of finding such permutations is shown to be substantially simplifiable in the case of self-dual codes in general, and for self-dual codes of sufficiently high minimum distance it is shown that it is frequently possible to deduce the existence of these permutations directly from the parameters of the code.A new and tighter link between generalized Hamming weights and trellis representations is demonstrated: for some self-dual codes, knowledge of one of the generalized Hamming weights is sufficient to determine the entire optimal state complexity profile.These results are used to characterize the permutation-optimal trellises and generalized Hamming weights for all [32,16,8] binary self-dual codes and for several other codes. The numbers of uniformly efficient permutations for several codes, including the [24,12,8] Golay code and both [24,12,9] ternary self-dual codes, are found.