MinT - Information on Result #2226816

Information on Result #2226816

Linear OA(2²³², 572, F₂, 50) (dual of [572, 340, 51]-code), using 1 times truncation based on linear OA(2²³³, 573, F₂, 51) (dual of [573, 340, 52]-code), using

constructionÂ X applied to C_e(50) âŠ‚ C_e(40) [i] based on
1. linear OA(2²⁰⁸, 512, F₂, 51) (dual of [512, 304, 52]-code), using an extension C_e(50) of the primitive narrow-sense BCH-code C(I) with length 511Â = 2⁹âˆ’1, defining interval IÂ =Â [1,50], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 51 [i]
2. linear OA(2¹⁷², 512, F₂, 41) (dual of [512, 340, 42]-code), using an extension C_e(40) of the primitive narrow-sense BCH-code C(I) with length 511Â = 2⁹âˆ’1, defining interval IÂ =Â [1,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]
3. linear OA(2²⁵, 61, F₂, 9) (dual of [61, 36, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²⁵, 63, F₂, 9) (dual of [63, 38, 10]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OA(2²³⁴, 574, F₂, 50) (dual of [574, 340, 51]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(2²³⁵, 575, F₂, 50) (dual of [575, 340, 51]-code)	[i]	Code Embedding in Larger Space
3	Linear OA(2²³⁶, 580, F₂, 50) (dual of [580, 344, 51]-code)	[i]	VarÅ¡amovâ€“Edel Lengthening
4	Linear OA(2²³⁴, 575, F₂, 50) (dual of [575, 341, 51]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
5	Linear OA(2²³⁵, 577, F₂, 50) (dual of [577, 342, 51]-code)	[i]
6	Linear OA(2²³⁷, 581, F₂, 50) (dual of [581, 344, 51]-code)	[i]
7	Linear OA(2²³⁸, 583, F₂, 50) (dual of [583, 345, 51]-code)	[i]
8	Linear OOA(2²³², 286, F₂, 2, 50) (dual of [(286, 2), 340, 51]-NRT-code)	[i]	OOA Folding
9	Linear OOA(2²³², 190, F₂, 3, 50) (dual of [(190, 3), 338, 51]-NRT-code)	[i]	OOA Folding