MinT - Information on Result #3265526

Information on Result #3265526

Digital (58, 77, 59051)-net over F₂₇, using 27¹ times duplication based on digital (57, 76, 59051)-net over F₂₇, using

net defined by OOA [i] based on linear OOA(27⁷⁶, 59051, F₂₇, 19, 19) (dual of [(59051, 19), 1121893, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(27⁷⁶, 531460, F₂₇, 19) (dual of [531460, 531384, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(27⁷⁶, 531461, F₂₇, 19) (dual of [531461, 531385, 20]-code), using
    - constructionÂ X applied to C([0,9]) âŠ‚ C([0,7]) [i] based on
      1. linear OA(27⁷³, 531442, F₂₇, 19) (dual of [531442, 531369, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 27⁸âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      2. linear OA(27⁵⁷, 531442, F₂₇, 15) (dual of [531442, 531385, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 27⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
      3. linear OA(27³, 19, F₂₇, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,27) or 19-cap in PG(2,27)), using
        discarding factors / shortening the dual code based on linear OA(27³, 27, F₂₇, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
        Reedâ€“Solomon code RS(24,27) [i]

Mode: Constructive and 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.