Abstract
Quasi-cyclic codes of length 5 ℓ and index ℓ over F q are obtained from a pair of codes over, respectively, F q and F q 4 , by a combinatorial construction called here the quintic construction. They enjoy a designed trellis description and a suboptimal coset decoding algorithm. They are shown to be cyclic when the component codes are cyclic of odd length coprime to 5 . Extremal binary self-dual quintic codes are constructed in lengths 60 and 70 by a randomized algorithm.
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