MinT - Information on Result #1194538

Information on Result #1194538

Digital (107, 132, 4931)-net over F₉, using net defined by OOA based on linear OOA(9¹³², 4931, F₉, 27, 25) (dual of [(4931, 27), 133005, 26]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(9¹³², 19725, F₉, 3, 25) (dual of [(19725, 3), 59043, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9¹³², 19727, F₉, 3, 25) (dual of [(19727, 3), 59049, 26]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(9²⁰, 40, F₉, 3, 12) (dual of [(40, 3), 100, 13]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,107P) [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
        a function field by SÃ©mirat [i]
    2. linear OOA(9¹¹², 19687, F₉, 3, 25) (dual of [(19687, 3), 58949, 26]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(9¹¹², 59061, F₉, 25) (dual of [59061, 58949, 26]-code), using
        constructionÂ X applied to C([0,12]) âŠ‚ C([0,11]) [i] based on
        linear OA(9¹¹¹, 59050, F₉, 25) (dual of [59050, 58939, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 9¹⁰âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
        linear OA(9¹⁰¹, 59050, F₉, 23) (dual of [59050, 58949, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 9¹⁰âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (BCH-bound) [i]
        linear OA(9¹, 11, F₉, 1) (dual of [11, 10, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(9¹, s, F₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.