Upper and lower bounds are presented for the maximal possible size of mixed binary/ternary error-correcting codes. A table up to length 13 is included. The upper bounds are obtained by applying the linear programming bound to the product of two association schemes. The lower bounds arise from a number of different constructions.

A binary code $C \subseteq \mathbb{F}_2^n$ with M codewords is called an $( n,M,r,u )$ multiple covering of the farthest-off points (MCF) if the Hamming spheres of radius r centered at the codewords cover the whole space $\mathbb{F}_2^n $ and every $x \in \mathbb{F}_2^n $ such that $d( x,C ) = r$ is covered by at least $\mu $ codewords. The minimum possible cardinality $F( n,r,\mu )$ of such a code is studied and tables of upper bounds on $F ( n,r,\mu )$ for $n \leq 16,r \leq 4,\mu \leq 4$ are given.

The normality of binary codes is studied. The minimum cardinality of a binary code of length n with covering radius R is denoted by K(n,R). It is assumed that C is an (n,M)R code, that is, a binary code of length n with M codewords and covering radius R. It is shown that if C is an (n,M)1 code, then it is easy to find a normal (n,M)1 code by changing C in a suitable way, and that all the optimal (n,M)1 codes (i.e. those for which M=K(n,1)) are normal and their every coordinate is acceptable. It is shown that if C is an abnormal (n,M) code, then n>or=9, and an abnormal (9118)1 code which is the smallest abnormal code known at present, is constructed. Lower bounds on the minimum cardinality of a binary abnormal code of length n with covering radius 1 are derived, and it is shown that if an (n,M)1 code is abnormal, then M>or=96.>

The author obtains a binary code of length 18 which has 164*2/sup 6/=10496 codewords. The minimum distance of this code is three. Therefore, A(18,3)>or=10496. Shortening, the author obtains find a binary code of length 17 and minimum distance 3 which has 5248 codewords, showing that A(17,3)>or=5248.>

A novel method for constructing normal binary nonlinear covering codes is presented. The construction improves several upper bounds on K(n,R), the minimum cardinality of a binary code of length n and covering radius R.>