Codes with a Circulant Parity Check Matrix

Abstract

In this work we study codes characterized by the property that their parity check matrix is circulant, i.e., that rows are obtained as all the distinct cyclic shifts of the first row. For these codes, we give simple expressions for their dimension and for a lower bound on their minimum distance. We also present an ${\tt O}(nd)$ algorithm to solve the problem of deciding whether codes satisfying given constraints on their block length $n$, dimension $k$ and minimum distance $d$ exist in this class. Some long binary codes found using this algorithm are compared against the Varshamov-Gilbert bound.

Cite this paper

@article{servetto1998codes,
  title = {{Codes with a Circulant Parity Check Matrix}},
  author = {Servetto, S.D. and Blahut, Richard E.},
  year = {1998}
}

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