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2008
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Coprimitive sets and inextendable codes

9 years 2 months ago
Coprimitive sets and inextendable codes
Complete (n, r)-arcs in PG(k - 1, q) and projective (n, k, n - r)q-codes that admit no projective extensions are equivalent objects. We show that projective codes of reasonable length admit only projective extensions. Thus, we are able to prove the maximality of many known linear codes. At the same time our results sharply limit the possibilities for constructing long nonlinear codes. We also show that certain short linear codes are maximal. The methods here may be just as interesting as the results. They are based on the Bruen-Silverman model of linear codes (see [1, 2, 9] and [15]) as well as the theory of R?edei blocking sets first introduced in [8].
T. L. Alderson, Aiden A. Bruen
Added 25 Dec 2009
Updated 25 Dec 2009
Type Conference
Year 2008
Where DCC
Authors T. L. Alderson, Aiden A. Bruen
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