NEW BINARY CODING RESULTS BY CIRCULANTS

The Introduction contains a new circulant echelon canonical form for the perfect (23,12) Golay code and some tentative conclusions are suggested. Section I gives an account of the properties of circulant matrices A, and a number of lemmas that make it possible to determine the minimum weight of codes generated by the rows of a matrix of the form EA. In Section II, it is shown that many quadratic residue codes are almost of this form. The following new minimum weight results are obtained: For the (79, 40) code, w = 15; (103,52), w = 19; (151, 76), w = 19; (89,45), W = 17 and for (113, 57), w = 15. In Section III, high-quality (noncyclic) group codes are constructed by means of circulants. In some cases a definite improvement is obtained on the best previously known Bose-Chaudhuri-Hocquenghem cyclic codes (including the (31, 16) code). Methods of coding and decoding circulant codes are not discussed. © 1969, IEEE. All Rights Reserved.