MinT - Information on Result #1747986

Information on Result #1747986

Digital (37, 68, 2050)-net over F₁₂₈, using net defined by OOA based on linear OOA(128⁶⁸, 2050, F₁₂₈, 36, 31) (dual of [(2050, 36), 73732, 32]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(128⁶⁸, 8201, F₁₂₈, 4, 31) (dual of [(8201, 4), 32736, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(128⁶⁸, 8204, F₁₂₈, 4, 31) (dual of [(8204, 4), 32748, 32]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(128⁶⁸, 8204, F₁₂₈, 2, 31) (dual of [(8204, 2), 16340, 32]-NRT-code), using
    - OOA 2-folding [i] 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
        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]
        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]
        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: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.