Some new results for optimal ternary linear codes

Bouyukliev, Iliya; Simonis, Juriaan

doi:10.1109/18.992814

Cited by 26 publications

(22 citation statements)

References 12 publications

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“…More information on this approach can be found in [2]. The subcodes through which the codes are constructed must also be self-orthogonal.…”

Section: Preliminaries the Euclidean Inner Product Of Two Vectorsmentioning

confidence: 99%

Classification of Self-Orthogonal Codes over \boldmath$\F_3$ and \boldmath$\F_4$

Bouyukliev¹,

Östergård²

2005

SIAM J. Discrete Math.

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Several methods for classifying self-orthogonal codes up to equivalence are presented. These methods are used to classify self-orthogonal codes with largest possible minimum distance over the fields F 3 and F 4 for lengths n ≤ 29 and small dimensions (up to 6). Some properties of the classified codes are also presented. In particular, an extensive collection of quantum error-correcting codes is obtained.

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“…More information on this approach can be found in [2]. The subcodes through which the codes are constructed must also be self-orthogonal.…”

Section: Preliminaries the Euclidean Inner Product Of Two Vectorsmentioning

confidence: 99%

Classification of Self-Orthogonal Codes over \boldmath$\F_3$ and \boldmath$\F_4$

Bouyukliev¹,

Östergård²

2005

SIAM J. Discrete Math.

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“…More advanced strategies use ideas from [3] and [11] which give a canonical labelling and the automorphism group of the codes. For more information we refer to [5].…”

Section: Computational Resultsmentioning

confidence: 99%

Projective two-weight codes with small parameters and their corresponding graphs

et al. 2006

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“…It is easy to see that F 0 forms a hyperplane of Σ if Φ 1 = 0 and gcd(d, q) = 1 so that Theorem 2.1 holds. For example, let C 1 be the Golay [11,6,5] 3 code with a generator matrix Then Φ 1 = 0 from its weight distribution 0 1 5 132 6 132 8 330 9 110 11 24 . Since…”

Section: Lemma 37 F Forms a Blocking Set With Respect To Lines In σmentioning

confidence: 99%

“…A problem which has received a fair amount of attention is that of deriving conditions purely on the weight distribution of a code such that the extendability is guaranteed. [5]). Comparatively, our extension to find an [n + l, k, d + s] q code from C is called extension up to length [5] or lengthening [2].…”

Section: Introductionmentioning

confidence: 99%