MinT - Information on Result #903433

Information on Result #903433

Linear OOA(49⁵⁵, 1257, F₄₉, 2, 21) (dual of [(1257, 2), 2459, 22]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(49¹¹, 51, F₄₉, 2, 10) (dual of [(51, 2), 91, 11]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 11, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]
linear OOA(49⁴⁴, 1206, F₄₉, 2, 21) (dual of [(1206, 2), 2368, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(49⁴⁴, 2412, F₄₉, 21) (dual of [2412, 2368, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(49⁴⁴, 2413, F₄₉, 21) (dual of [2413, 2369, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,8]) [i] based on
      1. linear OA(49⁴¹, 2402, F₄₉, 21) (dual of [2402, 2361, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402Â | 49⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      2. linear OA(49³³, 2402, F₄₉, 17) (dual of [2402, 2369, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402Â | 49⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
      3. linear OA(49³, 11, F₄₉, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,49) or 11-cap in PG(2,49)), using
        discarding factors / shortening the dual code based on linear OA(49³, 49, F₄₉, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), using
        Reedâ€“Solomon code RS(46,49) [i]

Mode: Constructive and 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

None.