A decoding method for binary two-error correcting cyclic codes whose generator polynomials have at most two irreducible factors is presented. This class includes binary narrow-sense BCH codes with designed distance 5. The decoding algorithm uses the Zech logarithm for the finite field in which the roots of the code lie.>

A divisible code is a linear code whose word weights have a common divisor larger than one. If the divisor is a power of the field characteristic, there is a simple bound on the dimension of the code in terms of its weight range. When this bound is applied to the subcode of words with weight divisible by four in a type I binary self-dual code. It yields an asymptotic improvement of the Conway-Sloane bound for self-dual codes.>

The structure of the supports of minimum weight words for the quadratic residue codes of length 27 is determined. This does not depend on the alphabet field. From the global code one can create a ternary code with the same structure.>

The exponent of a nonzero linear code over a finite field of characteristic p is the exponent in the highest power of p dividing the weights of all the codewords. If the code is a right ideal in a group algebra the exponent is related to invariant multilinear forms on the code. This expository paper presents recent results obtained from that relation, extending earlier work of Delsarte and McEliece.

Self-orthogonal ternary codes of minimum weight3may be analyzed in a straightforward manner using the theory of glueing introduced in earlier papers. The present paper describes a method for studying codes of minimum weight6: the supports of the words of weight6form what is called a center set. Associated with each center set is a graph, and all the graphs that can arise in this way are known. These techniques are used to classify the ternary self-dual codes of length20: there are24inequivalent codes,17of which are indecomposable. Six of the codes have minimum weight6.