# A bound on the minimum distance of quasi-cyclic codes

Güneri, Cem and Özbudak, Ferruh (2012) A bound on the minimum distance of quasi-cyclic codes. SIAM Journal on Discrete Mathematics, 26 (4). pp. 1781-1796. ISSN 0895-4801 (Print) 1095-7146 (Online)

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We give a general lower bound for the minimum distance of $q$-ary quasi-cyclic codes of length $m\ell$ and index $\ell$, where $m$ is relatively prime to $q$. The bound involves the minimum distances of constituent codes of length $\ell$ as well as the minimum distances of certain cyclic codes of length $m$ which are related to the fields over which the constituents are defined. We present examples which show that the bound is sharp in many instances. We also compare the performance of our bound against the bounds of Lally and Esmaeili-Yari.