We classify the self-dual Z/sub 4/ codes of all lengths from 10 through 15, extending the previous classification through length 9.

J.H. Conway and N.J.A. Sloane (see ibid., vol.36, no.6, p.1319-33, Nov. 1990) give weight enumerators of several self-dual codes with the highest possible minimal distance whose existence was not known. A generator matrix for one of these, a Type I (64, 32, 12) code, is given, proving its existence. The method of construction is described.>

An algorithm is developed that can be used to find, with a very low probability of error (10/sup -100/ or less in many cases), the minimum weights of codes far too large to be treated by any known exact algorithm. The probabilistic method is used to find minimum weights of all extended quadratic residue codes of length 440 or less. The probabilistic algorithm is presented for binary codes, but it can be generalized to codes over GF(q) with q>2.>

A new family of binary cyclic(n,(n + 1)/2)and(n,(n - 1)/2)codes are introduced, which include quadratic residue (QR) codes whennis prime. These codes are defined in terms of their idempotent generators, and they exist for all oddn = p_{1}^{a_{1}} p_{2}^{a_{2}} \cdots p_{r}^{a_{r}}where eachp_{i}is a prime\equiv \pm 1 \pmod{8}. Dual codes are identified. The minimum odd weight of a duadic(n,(n + 1)/2)code satisfies a square root bound. When equality holds in the sharper form of this bound, vectors of minimum weight hold a projective plane. The unique projective plane of order 8 is held by the minimum weight vectors in two inequivalent(73,37,9)duadic codes. All duadic codes of length less than127are identified, and the minimum weights of their extensions are given. One of the duadic codes of length113has greater minimum weight than the QR code of that length.

An algorithm is described for computing the automorphism group of an error correcting code. The algorithm determines the order of the automorphism group and produces a set of monomial permutations which generate the group. It has been implemented on a computer and has been used successfully on a great number of codes of moderate length.

A partial classification is given of the self-dual codes of length 24 over GF (3). The main results are as follows: there are exactly two codes with minimum Hamming distanced=9; most of the codes haved=6and are indecomposable; one code withd=6has a trivial automorphism group (this is the first such self-dual code that has been found); the codes generated by the59inequivalent24 \times 24Hadamard matrices have been investigated and there appear to be only nine inequivalent codes (two withd=9and seven withd=6); and in all there are27decomposable codes, at least96indecomposable codes withd=6, and the total number of inequivalent codes is at least140.