Double circulant quadratic residue codes
We give a lower bound for the minimum distance of double circulant binary quadratic residue codes for primes p equivalent to +/-3 (mod8). This bound improves on the square root bound obtained by Calderbank and Beenker, using a completely different technique. The key to our estimates is to apply a result by Helleseth, to which we give a new and shorter proof. Combining this result with the Weil bound leads to the improvement of the Calderbank and Beenker bound. For large primes p, their bound is of order root2p while our new improved bound is of order 2rootp. The results can be extended to any prime power q and the modifications of the proofs are briefly indicated.
quadratic residue code weil bound circulant code