Abstract
Double polycirculant codes are introduced here as a generalization of double circulant codes. When the matrix of the polyshift is a companion matrix of a trinomial, we show that such a code is isodual, hence formally self-dual. Numerical examples show that the codes constructed have optimal or quasi-optimal parameters amongst formally self-dual codes. Self-duality, the trivial case of isoduality, can only occur over \( {\mathbb {F}}_2\) in the double circulant case. Building on an explicit infinite sequence of irreducible trinomials over \({\mathbb {F}}_2,\) we show that binary double polycirculant codes are asymptotically good.
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Communicated by V. A. Zinoviev.
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This research is supported by National Natural Science Foundation of China (61672036), Excellent Youth Foundation of Natural Science Foundation of Anhui Province (1808085J20), Academic fund for outstanding talents in universities (gxbjZD03).
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Shi, M., Xu, L. & Solé, P. Construction of isodual codes from polycirculant matrices. Des. Codes Cryptogr. 88, 2547–2560 (2020). https://doi.org/10.1007/s10623-020-00799-8
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DOI: https://doi.org/10.1007/s10623-020-00799-8