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A computer calculation with Magma shows that there is no extremal self-dual binary code$C$of length 72 that has an automorphism group containing either the dihedral group of order 10, the elementary abelian group of order 9, or the cyclic group of order 7. Combining this with the known results in the literature, one obtains that the order of${\rm Aut}(C)$is either 5 or divides 24.

The performance of a turbo code with short block length depends critically on the interleaver design. There are two major criteria in the design of an interleaver: the distance spectrum of the code and the correlation between the information input data and the soft output of each decoder corresponding to its parity bits. This paper describes a new interleaver design for turbo codes with short block length based on these two criteria. A deterministic interleaver suitable for turbo codes is also described. Simulation results compare the new interleaver design to different existing interleavers.

The performance of a Turbo code depends on the interleaver design. There are two major criteria that can be considered in the design of an interleaver. Distance spectrum properties of the code and the correlation of the extrinsic information with the input data are the two major criteria in designing an interleaver. This paper describes a new interleaver design based on these two criteria. Simulation results compare the new interleaver design to different existing interleavers. The distance spectrum properties of the Turbo code are compared for different interleaver choices. A new solution to the interleaver edge effects is proposed here.