On self-dual codes over some prime fields

Betsumiya, Koichi; Georgiou, S.; Gulliver, T. Aaron; Harada, Masaaki; Koukouvinos, Christos

doi:10.1016/s0012-365x(02)00520-4

Cited by 78 publications

(103 citation statements)

References 10 publications

Supporting

Mentioning

103

Contrasting

Order By: Relevance

“…In this paper, we extend the results in [3], [7], [10], [12], where MDS self-dual codes over GF (q) of lengths up to 16 are given for certain (large) values of q. As it is very difficult to calculate the The work of Y. Lee was supported by KOSEF under Grant R01-2008-000-11721-0.…”

Section: Introductionmentioning

confidence: 77%

“…The DC code with first row 1, 1, 1, 0 is a Hermitian self-dual near-MDS [8,4,4] code over GF (16). Hermitian self-dual codes with parameters [6,3,4] or [8,4,4] were also constructed in [12].…”

Section: The Euclidean Inner Product Then the Following Matrixmentioning

confidence: 99%

“…In [3], a [16,8,9] MDS self-dual code over GF(23) was presented, and an MDS self-dual code of length 16 over GF(79) was given in [10]. No other MDS [16,8,9] self-dual codes over prime fields are known.…”

Section: The Euclidean Inner Product Then the Following Matrixmentioning

confidence: 99%

“…[14,7,8] code over GF (13) is constructed in [3]. It is also a Euclidean self-dual MDS [14,7,8] for a Euclidean self-dual near-MDS [14,7,7] code over GF (289).…”

Section: Ementioning

confidence: 99%

“…328]. Hence there has recently been great interest in the construction of (near) MDS self-dual codes over large fields (see [3], [7], [10], [12]). …”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

New MDS or Near-MDS Self-Dual Codes

Gulliver

Kim

Lee

2008

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

Abstract-We construct new MDS or near-MDS self-dual codes over large finite fields. In particular we show that there exists a Euclidean self-dual MDS code of length n = q over GF (q) whenever q = 2 m (m ≥ 2) using a Reed-Solomon (RS) code and its extension. It turns out that this MDS self-dual code is an extended duadic code. We construct Euclidean self-dual near-MDS codes of length n = q − 1 over GF (q) from RS codes when q ≡ 1 (mod 4) and q ≤ 113. We also construct many new MDS self-dual codes over GF (p) of length 16 for primes 29 ≤ p ≤ 113. Finally we construct Euclidean/Hermitian self-dual MDS codes of lengths up to 14 over GF (q 2 ) where q = 19, 23, 25, 27, 29.

show abstract

Section: Introductionmentioning

confidence: 77%

Section: The Euclidean Inner Product Then the Following Matrixmentioning

confidence: 99%

Section: The Euclidean Inner Product Then the Following Matrixmentioning

confidence: 99%

“…[14,7,8] code over GF (13) is constructed in [3]. It is also a Euclidean self-dual MDS [14,7,8] for a Euclidean self-dual near-MDS [14,7,7] code over GF (289).…”

Section: Ementioning

confidence: 99%

“…328]. Hence there has recently been great interest in the construction of (near) MDS self-dual codes over large fields (see [3], [7], [10], [12]). …”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

New MDS or Near-MDS Self-Dual Codes

Gulliver

Kim

Lee

2008

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

show abstract

MDS Self-Dual Codes over Large Prime Fields

Georgiou

Koukouvinos

2002

Finite Fields and Their Applications

View full text Add to dashboard Cite

Combinatorial designs have been used widely in the construction of self-dual codes. Recently a new method of constructing self-dual codes was established using orthogonal designs. This method has led to the construction of many new self-dual codes over small "nite "elds and rings. In this paper, we generalize this method by using generalized orthogonal designs, and we give another new method that creates and solves Diophantine equations over GF(p) in order to "nd suitable generator matrices for self-dual codes. We show that under the necessary conditions these methods can be applied as well to small and large "elds. We apply these two methods to study self-dual codes over GF(31) and GF(37). Using these methods we obtain some new maximum distance separable self-dual codes of small orders.2002 Elsevier Science (USA)

show abstract

Quasi-Cyclic Codes over $\mathbb{F}_{13}$

Gulliver

2011

Lecture Notes in Computer Science

View full text Add to dashboard Cite

On self-dual codes over some prime fields

Cited by 78 publications

References 10 publications

New MDS or Near-MDS Self-Dual Codes

New MDS or Near-MDS Self-Dual Codes

MDS Self-Dual Codes over Large Prime Fields

Quasi-Cyclic Codes over $\mathbb{F}_{13}$

Contact Info

Product

Resources

About