MinT - Information on Result #1614762

Information on Result #1614762

Linear OOA(128⁵⁶, 5315, F₁₂₈, 4, 27) (dual of [(5315, 4), 21204, 28]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(128⁵⁶, 5315, F₁₂₈, 3, 27) (dual of [(5315, 3), 15889, 28]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(128⁵⁶, 5465, F₁₂₈, 3, 27) (dual of [(5465, 3), 16339, 28]-NRT-code), using
- OOA 3-folding [i] based on linear OA(128⁵⁶, 16395, F₁₂₈, 27) (dual of [16395, 16339, 28]-code), using
  - discarding factors / shortening the dual code based on linear OA(128⁵⁶, 16396, F₁₂₈, 27) (dual of [16396, 16340, 28]-code), using
    - constructionÂ X applied to C([0,13]) âŠ‚ C([0,11]) [i] based on
      1. linear OA(128⁵³, 16385, F₁₂₈, 27) (dual of [16385, 16332, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (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(128³, 11, F₁₂₈, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,128) or 11-cap in PG(2,128)), using
        discarding factors / shortening the dual code based on linear OA(128³, 128, F₁₂₈, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
        Reedâ€“Solomon code RS(125,128) [i]

Mode: 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		This result only	Method
1	Linear OOA(128⁵⁶, 1328, F₁₂₈, 36, 27) (dual of [(1328, 36), 47752, 28]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row