MinT - Information on Result #1614465

Information on Result #1614465

Linear OOA(128³⁶, 6234, F₁₂₈, 4, 17) (dual of [(6234, 4), 24900, 18]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(128³⁶, 6234, F₁₂₈, 2, 17) (dual of [(6234, 2), 12432, 18]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(128³⁶, 8198, F₁₂₈, 2, 17) (dual of [(8198, 2), 16360, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128³⁶, 16396, F₁₂₈, 17) (dual of [16396, 16360, 18]-code), using
  - constructionÂ X applied to C([0,8]) âŠ‚ C([0,6]) [i] based on
    1. linear OA(128³³, 16385, F₁₂₈, 17) (dual of [16385, 16352, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
    2. linear OA(128²⁵, 16385, F₁₂₈, 13) (dual of [16385, 16360, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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(128³⁶, 3116, F₁₂₈, 20, 17) (dual of [(3116, 20), 62284, 18]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row