Maximal AMDS codes View Full Text


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Article Info

DATE

2008-04

AUTHORS

T. L. Alderson, A. A. Bruen

ABSTRACT

Complete (n, k)-arcs in PG(k − 1, q) and projective (n, k)q-AMDS codes that admit no projective extensions are equivalent objects. We show that projective AMDS codes of reasonable length admit only linear extensions. Thus, we are able to prove the maximality of many known linear AMDS codes. At the same time our results sharply limit the possibilities for constructing long nonlinear AMDS codes. We also show that certain short linear AMDS codes are maximal. Central to our approach is the Bruen–Silverman model of linear codes first introduced in Alderson (On MDS codes and Bruen–Silverman codes. Ph.D. Thesis, University of Western Ontario, 2002) and Alderson et al. (J. Combin. Theory Ser. A 114(6), 1101–1117, 2007). More... »

PAGES

87-98

References to SciGraph publications

  • 2004-06. On the Extendibility of Near-MDS Elliptic Codes in APPLICABLE ALGEBRA IN ENGINEERING, COMMUNICATION AND COMPUTING
  • 1996-10. Almost MDS codes in DESIGNS, CODES AND CRYPTOGRAPHY
  • 1955-12. Curve razionali normali ek-archi negli spazi finiti in ANNALI DI MATEMATICA PURA ED APPLICATA (1923 -)
  • 1988-10. On extendable planes, M.D.S. codes and hyperovals in PG(2, q), q=2t in GEOMETRIAE DEDICATA
  • 1995-11. On near-MDS codes in JOURNAL OF GEOMETRY
  • 1988-10. On M.D.S. codes, arcs inPG(n, q) withq even, and a solution of three fundamental problems of B. Segre in INVENTIONES MATHEMATICAE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00200-008-0058-0

    DOI

    http://dx.doi.org/10.1007/s00200-008-0058-0

    DIMENSIONS

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