MinT - Information on Result #1614877

Information on Result #1614877

Linear OOA(128⁶², 6045, F₁₂₈, 4, 29) (dual of [(6045, 4), 24118, 30]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(128⁶², 6045, F₁₂₈, 2, 29) (dual of [(6045, 2), 12028, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(128⁶², 8201, F₁₂₈, 2, 29) (dual of [(8201, 2), 16340, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128⁶², 16402, F₁₂₈, 29) (dual of [16402, 16340, 30]-code), using
  - constructionÂ X applied to C([0,14]) âŠ‚ C([0,11]) [i] based on
    1. linear OA(128⁵⁷, 16385, F₁₂₈, 29) (dual of [16385, 16328, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (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(128⁵, 17, F₁₂₈, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,128)), using
      - discarding factors / shortening the dual code based on linear OA(128⁵, 128, F₁₂₈, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
        Reedâ€“Solomon code RS(123,128) [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(128⁶², 1511, F₁₂₈, 36, 29) (dual of [(1511, 36), 54334, 30]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row