On Z4-Simplex Codes and Their Gray Images
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
On Linear Codes over$${\mathbb{Z}}_{2^{s}}$$
Designs, Codes and Cryptography
Minimal Trellis Construction for Finite Support Convolutional Ring Codes
ICMCTA '08 Proceedings of the 2nd international Castle meeting on Coding Theory and Applications
On minimality of convolutional ring encoders
IEEE Transactions on Information Theory
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We present an efficient algorithm for computing the minimal trellis for a group code over a finite abelian group, given a generator matrix for the code. We also show how to compute a succinct representation of the minimal trellis for such a code, and present algorithms that use this information to compute efficiently local descriptions of the minimal trellis. This extends the work of Kschischang and Sorokine (see ibid., vol.41, no.6, p.1926-37, 1995), who treated the case of linear codes over fields. An important application of our algorithms is to the construction of minimal trellises for lattices. A key step in our work is handling codes over cyclic groups C pα, where p is a prime. Such a code can be viewed as a module over the ring Zpα. Because of the presence of zero divisors in the ring, modules do not share the useful properties of vector spaces. We get around this difficulty by restricting the notion of linear combination to a p-linear combination, and by introducing the notion of a p-generator sequence, which enjoys properties similar to those of a generator matrix for a vector space