ACTA issues

On minimum distances of latin squares and the quadrangle criterion

Aleš Drápal

Acta Sci. Math. (Szeged) 70:1-2(2004), 3-11

Abstract. We give a new proof of a theorem of József Dénes: If $L_1$ and $L_2$ are distinct latin squares of order $n \ge2$, $n \notin\{4,6\} $, that satisfy the quadrangle criterion, then $L_1$ and $L_2$ differ in at least $2n$ entries.

AMS Subject Classification (1991): 20D60, 05B15

Keyword(s): multiplication table, quadrangle criterion, Hamming distance

Received December 12, 2002, and in revised form March 19, 2003. (Registered under 5794/2009.)