MinT - Information on Result #1615186

Information on Result #1615186

Linear OOA(128⁷⁶, 872835, F₁₂₈, 4, 25) (dual of [(872835, 4), 3491264, 26]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(128⁷⁶, 872835, F₁₂₈, 2, 25) (dual of [(872835, 2), 1745594, 26]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(128⁷⁶, 1048584, F₁₂₈, 2, 25) (dual of [(1048584, 2), 2097092, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128⁷⁶, 2097168, F₁₂₈, 25) (dual of [2097168, 2097092, 26]-code), using
  - constructionÂ X applied to C([0,12]) âŠ‚ C([0,10]) [i] based on
    1. linear OA(128⁷³, 2097153, F₁₂₈, 25) (dual of [2097153, 2097080, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
    2. linear OA(128⁶¹, 2097153, F₁₂₈, 21) (dual of [2097153, 2097092, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
    3. linear OA(128³, 15, F₁₂₈, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,128) or 15-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(128⁷⁶, 290944, F₁₂₈, 28, 25) (dual of [(290944, 28), 8146356, 26]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row