Let d/sub 3/(n,k) be the maximum possible minimum Hamming distance of a ternary [n,k,d]-code for given values of n and k. We describe a package for code extension and use this to prove some new exact values of d/sub 3/(n,k). Moreover, we classify the ternary [n,k,d/sub 3/(n,k)]-codes for some values of n and k.

The article gives a new condition for a q-ary linear code of length n and minimum distance d to be extendable to a code of the same dimension, length n+1, and minimum distance >d.

Let n(k, d) be the smallest integer n for which a binary linear code of length n, dimension k, and minimum distance d exists. Using the residual code technique, the MacWilliams identities and the weight distribution of appropriate Reed-Muller codes, we prove that n(9, 64)=133, n(9, 120)/spl ges/244, n(9, 124)=252, and n(9, 184)=371. We also show that puncturing a known [322, 9, 160]-code yields length-optimal codes with parameters [319, 9, 158], [315, 9, 156], and [312, 9, 154].

If C is a binary linear code, one may choose a subset S of C, and form a new code C/sub S//sup T/ which is the row space of the matrix having the elements of S as its columns. One way of picking S is to choose a subgroup H of Aut(C) and let S be some H-stable subset of C. Using (primarily) this method for picking S, we obtain codes with record-breaking parameters [92,8,44], [105,8,50], [108,8,52], [79,9,36], [123,9,58], [130,9,62], [175,9,84], [242,9,118], and [245,9,120].

A new family of metrics is introduced. Each of these is defined by a spanning set F of linear subspaces of a finite vector space. The norm of a vector is defined as the size of a minimal subset of F whose span contains this vector. Some examples and applications are presented. A-class of Varshamov-Gilbert bound based F-metrics is introduced. Connections with combinatorial metrics are discussed.

The words of a binary linear /spl lsqb/n, k/spl rsqb/ code C whose weights belong to a given subset I/spl sub//spl lcub/0,1,...,n/spl rcub/ constitute a word in a certain Reed-Muller code /spl Rfr//spl Mfr/(r, k). Appropriate choices of I result in low values of the order r and thus yield restrictions on the weight distribution of C.>

The nonexistence of a binary linear (15,6) code with covering radius 3 is proved by geometrically based arguments. The author also considers the wider application of the techniques.>

That binary even[25,15,6]codes do not exist is proved by passing from coding theory to{\bf F}_{2}-affine geometry; all25-sets in{\bf F}^{9}_{2}are shown to contain affine planes.