In previous work by Huffman and by Yorgov (1983), a decomposition theory of self-dual linear codes C over a finite field F/sub q/ was given when C has a permutation automorphism of prime order r relatively prime to q. We extend these results to linear codes over the Galois ring Z/sub 4/ and apply the theory to Z/sub 4/-codes of length 24. In particular we obtain 42 inequivalent [24,12] Z/sub 4/-codes of minimum Euclidean weight 16 which lead to 42 constructions of the Leech lattice.

We prove that, up to equivalence, there is a unique extremal quaternary Hermitian self-dual code of length 18, and that there are two inequivalent extremal quaternary Hermitian self-dual codes of length 20.

We give the full automorphism groups as groups of semiaffine transformations, of the extended generalized quadratic residue codes. We also present a proof of the Gleason-Prange theorem for the extended generalized quadratic residue codes that relies only on their definition and elementary theory of linear characters.>

The extremal self-dual ternary codes of lengths 28, 32, and 36 with monomial automorphisms of prime order r>or=5 and of length 40 with monomial automorphisms of prime order r>5 are enumerated. For each length and prime considered, all inequivalent extremal codes with an automorphism of that order are found.>

For pt.I see ibid., vol.36, no.3, p.651-60 (1990). A general decomposition theorem is applied to find all extremal self-dual quaternary codes of lengths 18 to 28 that have a nontrivial monomial automorphism of order a power of 3. Techniques to distinguish these codes are also presented. The author presents situations in which the equivalence of the codes under consideration can be decided.>

A general decomposition theorem is given for self-dual codes over finite fields that have a permutation automorphism of a given form. Such a code can be decomposed as a direct sum of subcodes that may be viewed as shorter-length codes over extension fields where the dual of each direct summand is also a direct summand. Situations in which it is easy to distinguish such codes are also presented. These results are used to enumerate some of the extremal quaternary self-dual codes of lengths 18, 20, 22, 26 and 28.>

A general theory is given for examining quaternary self-dual codes having monomial automorphisms of orders that are a power of 3. A theory of decomposing such codes is given and applications of this theory are described. This work extends similar work when the codes have nontrivial odd-order permutation automorphisms.>

A general decomposition theorem is given for codes over finite fields which have an automorphism of a given type. Such codes can be decomposed as direct sums of subcodes which may be viewed as shorter length codes over extension fields. If such a code is self-dual, sometimes the subcodes are also. This decomposition is applied to prove that the self-dual (24, 12, 10) quaternary code has no automorphism of order 3. This decomposition is also applied to count the number of equivalent (2r, r) and (2r+2r+1) self-dual binary codes with an automorphism of prime order r.>

We prove that there does not exist a[72,36,16]doubly even code with an automorphism of order11. If such a code exists, it can be decomposed as a direct sum of two codes; one can be viewed as a self-dual[12,6,4]binary code and the other a self-dual[6,3,4]code overF_{1024}. This is shown to be impossible.

Codes possessing certain types of automorphisms are examined. In one case, the code can be decomposed as a direct sum of two subcodes, which can be viewed as shorter length codes. In a second case, the code itself corresponds to a shorter length code. Related results and applications are given.

General results on automorphisms of self-dual binary codes are given. These results are applied to the study of extremal self-dual doubly even binary codes of length48. The main theorem proved is that an extremal self-dual doubly even code of length48with a nontrivial automorphism of odd order is equivalent to the extended quadratic residue code. Interesting constructions of the binary extended Golay code as well as a conjecture about a possible connection between an extremal self-dual doubly even code of length72and an extremal quaternary code of length24arc yielded by techniques used in the proof.