MinT - Information on Result #731581

Information on Result #731581

Linear OA(16⁶⁴, 131096, F₁₆, 15) (dual of [131096, 131032, 16]-code), using trace code based on linear OA(256³², 65548, F₂₅₆, 15) (dual of [65548, 65516, 16]-code), using

constructionÂ X applied to C([0,7]) âŠ‚ C([0,5]) [i] based on
1. linear OA(256²⁹, 65537, F₂₅₆, 15) (dual of [65537, 65508, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
2. linear OA(256²¹, 65537, F₂₅₆, 11) (dual of [65537, 65516, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (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(16⁶⁵, 131097, F₁₆, 15) (dual of [131097, 131032, 16]-code)	[i]	Code Embedding in Larger Space
2	Linear OOA(16⁶⁴, 131096, F₁₆, 2, 15) (dual of [(131096, 2), 262128, 16]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Digital (49, 64, 131096)-net over F₁₆	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(16⁶⁴, 65548, F₁₆, 2, 15) (dual of [(65548, 2), 131032, 16]-NRT-code)	[i]	OOA Folding
5	Linear OOA(16⁶⁴, 18727, F₁₆, 15, 15) (dual of [(18727, 15), 280841, 16]-NRT-code)	[i]	OOA Folding and Stacking with Additional Row