Math @ Duke

Publications [#236044] of Robert Calderbank
Papers Published
 Calderbank, AR; McGuire, G, Z_{4}linear codes obtained as projections of Kerdock and DelsarteGoethals codes,
Linear Algebra and its Applications, vol. 226228 no. C
(1995),
pp. 647665, ISSN 00243795 [doi]
(last updated on 2018/03/22)
Abstract: The Kerdock and DelsarteGoethals codes can be very simply constructed as binary images under a certain natural map, called the Gray map, of linear codes over Z4, the integers modulo 4. We consider the Gray images of linear codes over Z4 obtained from the Kerdock and DelsarteGoethals codes by projection on a hyperplane. For m odd, certain Gray images have the same weight distribution as duals of extended binary BCH codes of length 2m, but are not equivalent to these codes. Inequivalence follows from a general theorem identifying binary linear codes that are not Gray images of linear codes over Z4. © 1995.


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