A characterization of a (56,28) extremal self-dual code (Corresp.)

Bhargava, V.K.; Young, George M.; Bhargava, Aniruddha

doi:10.1109/tit.1981.1056308

Cited by 9 publications

(12 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition, 4 and 9 more inequivalent extremal doubly-even [56, 28, 12] codes can be found in [3] and [6], respectively. Note that the first code among the six codes found in [3] is equivalent to the code in [2] which has an automorphism of order 13 [3] and the 5th and 6th codes are equivalent [8]. As described in Remarks 3.5 and 3.8, there are six pairs of two equivalent codes among the 1137 codes in [6], Propositions 3.4 and 3.6.…”

Section: Extremal Doubly-even Self-dual Codesmentioning

confidence: 99%

Self-Orthogonal 3-(56,12,65) Designs and Extremal Doubly-Even Self-Dual Codes of Length 56

Harada

2006

Des Codes Crypt

View full text Add to dashboard Cite

In this paper, we show that the code generated by the rows of a block-point incidence matrix of a self-orthogonal 3-(56, 12, 65) design is a doubly-even self-dual code of length 56. As a consequence, it is shown that an extremal doubly-even self-dual code of length 56 is generated by the codewords of minimum weight. We also demonstrate that there are more than one thousand inequivalent extremal doubly-even self-dual [56, 28,12] codes. This result shows that there are more than one thousand non-isomorphic self-orthogonal 3-(56, 12, 65) designs.

show abstract

Section: Extremal Doubly-even Self-dual Codesmentioning

confidence: 99%

Self-Orthogonal 3-(56,12,65) Designs and Extremal Doubly-Even Self-Dual Codes of Length 56

Harada

2006

Des Codes Crypt

View full text Add to dashboard Cite

show abstract

“…Therefore we omit the term "binary". Bhargava, Young and Bhargava [5] constructed an extremal doubly even [56, 28, 12] code. Yorgov [26] proved that there exist exactly 16 inequivalent extremal doubly even [56, 28, 12] codes with automorphisms of order 13.…”

Section: Extremal Binary Doubly Even [56 28 12] Codesmentioning

confidence: 99%

“…Yorgov [26] proved that there exist exactly 16 inequivalent extremal doubly even [56, 28, 12] codes with automorphisms of order 13. As stated in [15], one of the 16 codes in [26] is equivalent to the code in [5]. Bussemarker and Tonchev [8] constructed 6 extremal doubly even [56, 28, 12] codes.…”

Section: Extremal Binary Doubly Even [56 28 12] Codesmentioning

confidence: 99%

See 1 more Smart Citation

Construction for both self-dual codes and LCD codes

Ishizuka¹,

Saito²

2023

AMC

View full text Add to dashboard Cite

From a given [n, k] code C, we give a method for constructing many [n, k] codes C' such that the hull dimensions of C and C' are identical. This method can be applied to constructions of both self-dual codes and linear complementary dual codes (LCD codes for short). Using the method, we construct 661 new inequivalent extremal doubly even [56, 28, 12] codes. Furthermore, constructing LCD codes by the method, we improve some of the previously known lower bounds on the largest minimum weights of binary LCD codes of length 26 ≤ n ≤ 40.

show abstract

“…[3], which have covering radius 10. We denote the code in [3] by BY B. Ozeki [17] We verified by Magma [4] that the code E has automorphism group of order 9.…”

Section: Introductionmentioning

confidence: 99%

On s-extremal singly even self-dual [24k+ 8,12k+ 4,4k+ 2] codes

Harada¹,

Munemasa²

2017

Finite Fields and Their Applications

View full text Add to dashboard Cite

A relationship between s-extremal singly even self-dual [24k + 8, 12k + 4, 4k + 2] codes and extremal doubly even self-dual [24k + 8, 12k + 4, 4k + 4] codes with covering radius meeting the Delsarte bound, is established. As an example of the relationship, s-extremal singly even self-dual [56, 28,10] codes are constructed for the first time. In addition, we show that there is no extremal doubly even self-dual code of length 24k+8 with covering radius meeting the Delsarte bound for k ≥ 137. Similarly, we show that there is no extremal doubly even self-dual code of length 24k + 16 with covering radius meeting the Delsarte bound for k ≥ 148. We also determine the covering radii of some extremal doubly even self-dual codes of length 80.

show abstract

A characterization of a (56,28) extremal self-dual code (Corresp.)

Cited by 9 publications

References 5 publications

Self-Orthogonal 3-(56,12,65) Designs and Extremal Doubly-Even Self-Dual Codes of Length 56

Self-Orthogonal 3-(56,12,65) Designs and Extremal Doubly-Even Self-Dual Codes of Length 56

Construction for both self-dual codes and LCD codes

On s-extremal singly even self-dual [24k+ 8,12k+ 4,4k+ 2] codes

Contact Info

Product

Resources

About