MinT - Information on Result #2226885

Information on Result #2226885

Linear OA(2²⁴¹, 572, F₂, 52) (dual of [572, 331, 53]-code), using 1 times truncation based on linear OA(2²⁴², 573, F₂, 53) (dual of [573, 331, 54]-code), using

constructionÂ X applied to C_e(52) âŠ‚ C_e(42) [i] based on
1. linear OA(2²¹⁷, 512, F₂, 53) (dual of [512, 295, 54]-code), using an extension C_e(52) of the primitive narrow-sense BCH-code C(I) with length 511Â = 2⁹âˆ’1, defining interval IÂ =Â [1,52], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 53 [i]
2. linear OA(2¹⁸¹, 512, F₂, 43) (dual of [512, 331, 44]-code), using an extension C_e(42) of the primitive narrow-sense BCH-code C(I) with length 511Â = 2⁹âˆ’1, defining interval IÂ =Â [1,42], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 43 [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(2²⁴³, 574, F₂, 52) (dual of [574, 331, 53]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(2²⁴⁴, 575, F₂, 52) (dual of [575, 331, 53]-code)	[i]	Code Embedding in Larger Space
3	Linear OA(2²⁴², 574, F₂, 52) (dual of [574, 332, 53]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
4	Linear OA(2²⁴³, 576, F₂, 52) (dual of [576, 333, 53]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
5	Linear OOA(2²⁴¹, 286, F₂, 2, 52) (dual of [(286, 2), 331, 53]-NRT-code)	[i]	OOA Folding
6	Linear OOA(2²⁴¹, 190, F₂, 3, 52) (dual of [(190, 3), 329, 53]-NRT-code)	[i]	OOA Folding