충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제23권1호
  • /
  • Pages.91-98
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  • 2010
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
권호 표지

TRIPLE CIRCULANT CODES BASED ON QUADRATIC RESIDUES

  • Han, Sunghyu (School of Liberal Arts Korea University of Technology and Education)
  • 투고 : 2009.11.10
  • 심사 : 2010.02.16
  • 발행 : 2010.03.30
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초록

One of the most interesting classes of algebraic codes is the class of quadratic residue (QR) codes over a finite field. A natural construction doubling the lengths of QR codes seems to be the double circulant constructions based on quadratic residues given by Karlin, Pless, Gaborit, et. al. In this paper we define a class of triple circulant linear codes based on quadratic residues. We construct many new optimal codes or codes with the highest known parameters using this construction. In particular, we find the first example of a ternary [58, 20, 20] code, which improves the previously known highest minimum distance of any ternary [58, 20] codes.

키워드

참고문헌

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