MinT - Information on Result #731629

Information on Result #731629

Linear OA(16⁹⁶, 131096, F₁₆, 23) (dual of [131096, 131000, 24]-code), using trace code based on linear OA(256⁴⁸, 65548, F₂₅₆, 23) (dual of [65548, 65500, 24]-code), using

constructionÂ X applied to C([0,11]) âŠ‚ C([0,9]) [i] based on
1. linear OA(256⁴⁵, 65537, F₂₅₆, 23) (dual of [65537, 65492, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (BCH-bound) [i]
2. linear OA(256³⁷, 65537, F₂₅₆, 19) (dual of [65537, 65500, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
3. linear OA(256³, 11, F₂₅₆, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
  - discarding factors / shortening the dual code based on linear OA(256³, 256, F₂₅₆, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
    - Reedâ€“Solomon code RS(253,256) [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(16⁹⁷, 131097, F₁₆, 23) (dual of [131097, 131000, 24]-code)	[i]	Code Embedding in Larger Space
2	Linear OOA(16⁹⁶, 131096, F₁₆, 2, 23) (dual of [(131096, 2), 262096, 24]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Digital (73, 96, 131096)-net over F₁₆	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OA(16⁹⁷, 131098, F₁₆, 23) (dual of [131098, 131001, 24]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
5	Linear OOA(16⁹⁶, 65548, F₁₆, 2, 23) (dual of [(65548, 2), 131000, 24]-NRT-code)	[i]	OOA Folding