Publications [#236006] of Robert Calderbank

Journal articles or Book chapters PUBLISHED

1. Calderbank, R, A Square Root Bound on the Minimum Weight in Quasi-Cyclic Codes, IEEE Transactions on Information Theory, vol. 29 no. 3 (January, 1983), pp. 332-337, Institute of Electrical and Electronics Engineers (IEEE) [doi]
   (last updated on 2026/01/17)

   Abstract:
   We establish a square root bound on the minimum weight in the quasi-cyclic binary codes constructed by Bhargava, Tavares, and Shiva. The proof rests on viewing the codes as ideals in a group algebra over GF (4). Theorem 6 answers a question raised by F. J. MacWilliams and N. J. A. Sloane in The Theory of Error-Correcting Codes. Theorems 3, 4, and 5 provide information about the way the nonzero entries of a codeword of minimum weight are distributed among the coordinate positions. © 1983 IEEE