On isodual double polycirculant codes

11/09/2018

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by   Minjia Shi, et al.

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Double polycirculant codes are introduced here as a generalization of double circulant codes. They form a special class of quasi-polycyclic codes of index 2. 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 can only occur over _2 in the double circulant case. Building on the existence of infinitely many irreducible trinomials over _2 we show that double polycirculant binary codes satisfy the Varshamov-Gilbert bound for linear codes of rate one half. They are thus asymptotically good.