The equivalence of certain equidistant binary codes and symmetric bibds


We study equidistant codes of length 4k + 1 having (constant) weight 2k, and (constant) distance 2k between codewords. The maximum number of codewords is 4k; this can be attained if and only ifk = (u 2 +u)/2 (for some integeru) and there exists a ((2u 2 + 2u + 1,u 2, (u 2u)/2) — SBIBD. Also, one can construct such a code, with 4k − 1 codewords, from a (4k − 1, 2k − 1,k − 1) — SBIBD.

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Supported, in part by NSERC grants U0217 (D. R. Stinson), A3558 (G. H. J. van Rees).

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Stinson, D.R., van Rees, G.H.J. The equivalence of certain equidistant binary codes and symmetric bibds. Combinatorica 4, 357–362 (1984).

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AMS subject classification (1980)

  • 05 B 05