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A double circulant presentation for quadratic residue codes (Corresp.)

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1 Author(s)

For p eqiv pm 1 \pmod {8} there are two binary codes, Q(p) and N(p) , each an extended quadratic residue code of length p+1 and dimension (p+1)/2 . The existence of double circulant generator matrices for these codes is investigated. A possibly infinite family of primes p is presented for which Q(p) and N(p) must have double circulant generator matrices. Two counterexamples prove the construction is not always possible.

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IEEE Transactions on Information Theory  (Volume:26 ,  Issue: 2 )