With the Delsarte-MacWilliams inequalities as a starting point, an upper bound is obtained on the rate of a binary code as a function of its minimum distance. This upper bound is asymptotically less than Levenshtein's bound, and so also Elias's.
An alternating sign matrix is a square matrix such that (i) all entries are 1,-1, or 0, (ii) every row and column has sum 1, and (iii) in every row and column the nonzero entries alternate in sign. Striking numerical evidence of a connection between these matrices and the descending plane partitions introduced by Andrews (Invent. Math. 53 (1979), 193-225)… (More)