MinT - Information on Result #3265622

Information on Result #3265622

Digital (76, 101, 44288)-net over F₂₇, using 27¹ times duplication based on digital (75, 100, 44288)-net over F₂₇, using

net defined by OOA [i] based on linear OOA(27¹⁰⁰, 44288, F₂₇, 25, 25) (dual of [(44288, 25), 1107100, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(27¹⁰⁰, 531457, F₂₇, 25) (dual of [531457, 531357, 26]-code), using
  - discarding factors / shortening the dual code based on linear OA(27¹⁰⁰, 531461, F₂₇, 25) (dual of [531461, 531361, 26]-code), using
    - constructionÂ X applied to C([0,12]) âŠ‚ C([0,10]) [i] based on
      1. linear OA(27⁹⁷, 531442, F₂₇, 25) (dual of [531442, 531345, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 27⁸âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
      2. linear OA(27⁸¹, 531442, F₂₇, 21) (dual of [531442, 531361, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 27⁸âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (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.