The authors wish to thank G. D. Forney. Not only did he suggest the problem and act as a clearing house for the "Type II News Group," but also, perhaps most importantly, he provided constant encouragement during their search for a needle in a (huge) haystack. They are also grateful to N. J. A. Sloane for identifying B2 and to R. Kötter for an illuminating discussion on the Kötter-Vardy convolutional code.
An upper bound on the minimal state complexity of codes from the Hermitian function field and some of its subfields is derived. Coordinate orderings under which the state complexity of the codes is not above the bound are specified. For the self-dual Hermitian code it is proved that the bound coincides with the minimal state complexity of the code. Finally, it is shown that Hermitian codes over fields of characteristic 2 admit a recursive twisted squaring construction.Abstract-A class of linear codes with good parameters is constructed in this correspondence. It turns out that linear codes of this class are subcodes of the subfield subcodes of Goppa's geometry codes. In particular, we find 61 improvements on Brouwer's table [1] based on our codes.
The trellis complexity of the Preparata and Goethals codes is examined. It is shown that at least for a given set of permutations these codes are rectangular. Upper bounds on the state complexity profiles of the Preparata and Goethals codes are given. The upper bounds on the state complexity of the Preparata and Goethals codes are determined by the DLP of the extended primitive double-and tripleerror-correcting BCH codes, respectively. A twisted squaring construction for the Preparata and Goethals codes is given, based on the double-and triple-error-correcting extended primitive BCH codes, respectively.
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