Conference Paper

An efficient SAT encoding of circuit codes

Comput. Syst. Inst., ETH Zurich, Zurich
DOI: 10.1109/ISITA.2008.4895595 Conference: Information Theory and Its Applications, 2008. ISITA 2008. International Symposium on
Source: IEEE Xplore


Circuit codes in hypercubes are generalized snake-in-the-box codes and are used in analog-to-digital conversion devices. The construction of the longest known circuit codes is based on either an exhaustive search or an algorithm that restricts the search to the codes with periodic coordinate sequences. In this paper, we describe an efficient SAT encoding of circuit codes, which enabled us to obtain new circuit codes.

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    • "by eliminating half of its clauses, using an argument presented in [32]. "
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    Ed Wynn ·
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    ABSTRACT: Two new constructions are presented for coils and snakes in the hypercube. Improvements are made on the best known results for snake-in-the-box coils of dimensions 9, 10 and 11, and for some other circuit codes of dimensions between 8 and 13. In the first construction, circuit codes are generated from permuted copies of an initial transition sequence; the multiple copies constrain the search, so that long codes can be found relatively efficiently. In the second construction, two lower-dimensional paths are joined together with only one or two changes in the highest dimension; this requires a search for a permutation of the second sequence to fit around the first. It is possible to investigate sequences of vertices of the hypercube, including circuit codes, by connecting the corresponding vertices in an extended graph related to the hypercube. As an example of this, invertible circuit codes are briefly discussed.
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