Optimal four-dimensional codes over .
Jones, Chris, Matney, Angela, Ward, Harold (2006)
The Electronic Journal of Combinatorics [electronic only]
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Jones, Chris, Matney, Angela, Ward, Harold (2006)
The Electronic Journal of Combinatorics [electronic only]
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Landjev, Ivan, Rousseva, Assia (2008)
Serdica Journal of Computing
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In this paper, we prove the nonexistence of arcs with parameters (232, 48) and (233, 48) in PG(4,5). This rules out the existence of linear codes with parameters [232,5,184] and [233,5,185] over the field with five elements and improves two instances in the recent tables by Maruta, Shinohara and Kikui of optimal codes of dimension 5 over F5.
Okamoto, Kei (2008)
Serdica Journal of Computing
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We give the necessary and sufficient conditions for the extendability of ternary linear codes of dimension k ≥ 5 with minimum distance d ≡ 1 or 2 (mod 3) from a geometrical point of view.
Oya, Yusuke (2011)
Serdica Journal of Computing
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We prove the nonexistence of [g3(6, d), 6, d]3 codes for d = 86, 87, 88, where g3(k, d) = ∑⌈d/3i⌉ and i=0 ... k−1. This determines n3(6, d) for d = 86, 87, 88, where nq(k, d) is the minimum length n for which an [n, k, d]q code exists.
Kanazawa, Rie, Maruta, Tatsuya (2011)
The Electronic Journal of Combinatorics [electronic only]
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Clark, K. L., Hatfield, L. D., Key, J. D., Ward, H. N. (2003)
Advances in Geometry
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Maruta, Tatsuya (2013)
Serdica Journal of Computing
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Dedicated to the memory of S.M. Dodunekov (1945–2012)Abstract. Geometric puncturing is a method to construct new codes. ACM Computing Classification System (1998): E.4. ∗This research was partially supported by Grant-in-Aid for Scientific Research of Japan Society for the Promotion of Science under Contract Number 24540138.
Hamada, Noboru, Maruta, Tatsuya (2011)
Serdica Journal of Computing
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Let nq(k, d) denote the smallest value of n for which an [n, k, d]q code exists for given integers k and d with k ≥ 3, 1 ≤ d ≤ q^(k−1) and a prime or a prime power q. The purpose of this note is to show that there exists a series of the functions h3,q, h4,q, ..., hk,q such that nq(k, d) can be expressed. This research was partially supported by Grant-in-Aid for Scientific Research of Japan Society for the Promotion of Science under Contract Number 20540129.
Alderson, T.L., Bruen, A.A. (2008)
The Electronic Journal of Combinatorics [electronic only]
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Barwick, S.G. (1996)
Bulletin of the Belgian Mathematical Society - Simon Stevin
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H. S. Ruse (1935)
Compositio Mathematica
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