MinT - Information on Result #879198

Information on Result #879198

Linear OOA(128⁶⁸, 8204, F₁₂₈, 2, 31) (dual of [(8204, 2), 16340, 32]-NRT-code), using OOA 2-folding based on linear OA(128⁶⁸, 16408, F₁₂₈, 31) (dual of [16408, 16340, 32]-code), using

constructionÂ X applied to C([0,15]) âŠ‚ C([0,11]) [i] based on
1. linear OA(128⁶¹, 16385, F₁₂₈, 31) (dual of [16385, 16324, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
2. linear OA(128⁴⁵, 16385, F₁₂₈, 23) (dual of [16385, 16340, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (BCH-bound) [i]
3. linear OA(128⁷, 23, F₁₂₈, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,128)), using
  - discarding factors / shortening the dual code based on linear OA(128⁷, 128, F₁₂₈, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
    - Reedâ€“Solomon code RS(121,128) [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 OOA(128⁶⁸, 8204, F₁₂₈, 3, 31) (dual of [(8204, 3), 24544, 32]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(128⁶⁸, 8204, F₁₂₈, 4, 31) (dual of [(8204, 4), 32748, 32]-NRT-code)	[i]
3	Digital (37, 68, 8204)-net over F₁₂₈	[i]