A Note on Extended Quaternary Quadratic Residue Codes and Their Binary Images

For p a prime of the form 8 m ± 3, Karlin and MacWilliams (1972) have constructed some (2 p + 2, p + 1) codes which are the binary images of the ( p + 1, ( p + 1)/2) extended quadratic residue codes over GF (4). For p a prime of the form 8 m + 3, the (2 p + 2, p + 1) codes are equivalent to the codes proposed by Bhargava et al. (1974). In the related (2 p , p ) quasi-cyclic codes, the numbers of symmetrically placed odd weight words are equal.