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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 |E|A| . 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.
M. Karlin (Wed,) studied this question.
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