Algorithmic complexity in coding theory and the minimum distance problem
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Ordered Binary Decision Diagrams and Minimal Trellises
IEEE Transactions on Computers
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Gröbner Representations of Binary Matroids
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
A rate R = 5/20 hypergraph-based woven convolutional code with free distance 120
IEEE Transactions on Information Theory
On Trellis Structures for Reed-Muller Codes
Finite Fields and Their Applications
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The problem of minimizing the vertex count at a given time index in the trellis for a general (nonlinear) code is shown to be NP-complete. Examples are provided that show that (1) the minimal trellis for a nonlinear code may not be observable, i.e. some codewords may be represented by more than one path through the trellis and (2) minimizing the vertex count at one time index may be incompatible with minimizing the vertex count at another time index. A trellis produce is defined and used to construct trellises for sum codes. Minimal trellises for linear codes are obtained by forming the product of elementary trellises corresponding to the one-dimensional subcodes generated by atomic codewords. The structure of the resulting trellis is determined solely by the spans of the atomic codewords. A correspondence between minimal linear block code trellises and configurations of nonattacking rooks on a triangular chess board is established and used to show that the number of distinct minimal linear block code trellises is a Stirling number of the second kind. Various bounds on trellis size are reinterpreted in this context