Generalized quadratic-residue codes
At the 1975 CISM Summer School on Information Theory P. Camion (cf. ) introduced “global quadratic abelian codes” which are a generalization of (classical) quadratic residue codes (QR-codes). A year earlier H.N. Ward (cf. ) had used symplectic geometry to introduce a generalization of QR-codes. Both presentations rely heavily on abstract algebra. Essentially such codes (at least in the binary case) were introduced by Ph. Del-sarte in 1971 (cf. ) as codes generated by the adjacency matrices of finite miquelian inversive planes. Recently J.H. van Lint and F.J. Mac-Williams (cf. ) showed that the methods that are used to treat QR-codes can easily be generalized to give a completely analogous treatment of the so-called generalized quadratic residue codes (GQR-codes).
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- 1.Camion, P., Global Quadratic Abelian Codes, in Information Theory, CISM Courses and Lectures 219, G. Longo, ed., Springer-Verlag, Wien 1975.Google Scholar
- 4.van Lint J.H. and F.J. MacWilliams, Generalized Quadratic Residue Codes, IEEE Trans, on Information Theory 24 (1978).Google Scholar