The maximum of g/sub 2/ - d/sub 2/ for linear [n,k,d;q] codes C is studied. Here d/sub 2/ is the smallest size of the support of a two-dimensional subcode of C and g/sub 2/ is the smallest size of the support of a two-dimensional subcode of C which contains a codeword of weight d. For codes of dimension 4 or more, upper and lower bounds on the maximum of g/sub 2/-d/sub 2/ are given.

There are a large number of linear block codes satisfying the chain condition. Their weight hierarchies are called chain good and form an important group in classifying all possible weight hierarchies. In this paper, we present a series of new sufficient conditions to determine which kinds of sequences are chain good weight hierarchies. Our results are efficient for the determination of the chain good weight hierarchies with high dimension.

A constant-composition code is a special constant-weight code under the restriction that each symbol should appear a given number of times in each codeword. In this correspondence, we give a lower bound for the maximum size of the q-ary constant-composition codes with minimum distance at least 3. This bound is asymptotically optimal and generalizes the Graham-Sloane bound for binary constant-weight codes. In addition, three construction methods of constant-composition codes are presented, and a number of optimum constant-composition codes are obtained by using these constructions.

The weight hierarchy of a linear [n,k;q] code C over GF(q) is the sequence (d/sub 1/,d/sub 2/,/spl middot//spl middot//spl middot/,d/sub k/) where d/sub r/ is the smallest support of an r-dimensional subcode of C. An [n,k;q] code is extremal nonchain if, for any r and s, where 1/spl les/r

The weight hierarchy of a linear [n,k;q] code C over GF(q) is the sequence (d/sub 1/,d/sub 2/,...,d/sub k/) where d/sub r/ is the smallest support of an r-dimensional subcode of C. The codes of dimension 4 are collected in classes. For each class bounds and extremal codes are discussed.

The weight hierarchy of a linear [n,k;q] code C over GF(q) is the sequence (d/sub 1/,d/sub 2/,...d/sub k/) where d/sub /spl tau// is the smallest support of an /spl tau/-dimensional subcode of C. The possible weight hierarchies of [n,4;q] codes are studied. In particular, the possible weight hierarchies of [n,4;3] codes are determined.

Lower bounds for K(n, R), the minimal number of codewords of any binary code of length n and covering radius R, are improved. The definition of multiexcess is introduced. A technique combining van Wee's (1991) method and linear inequalities for covering codes is used. A revised table for K(n, R) (n/spl les/33, R/spl les/10) is given.>

The authors prove combinatorial lower bounds for K/sub q/(n,R), the minimal cardinality of any q-ary code of length n and covering radius R. Tables of lower bounds for K/sub q/(n,R) are presented for q=3, 4, 5.>