MinT - Information on Result #1377612

Information on Result #1377612

Linear OOA(9⁸⁹, 531450, F₉, 2, 15) (dual of [(531450, 2), 1062811, 16]-NRT-code), using OOA 2-folding based on linear OA(9⁸⁹, 1062900, F₉, 15) (dual of [1062900, 1062811, 16]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(9⁸⁸, 1062898, F₉, 15) (dual of [1062898, 1062810, 16]-code), using
  - trace code [i] based on linear OA(81⁴⁴, 531449, F₈₁, 15) (dual of [531449, 531405, 16]-code), using
    - constructionÂ X applied to C([0,7]) âŠ‚ C([0,6]) [i] based on
      1. linear OA(81⁴³, 531442, F₈₁, 15) (dual of [531442, 531399, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 81⁶âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
      2. linear OA(81³⁷, 531442, F₈₁, 13) (dual of [531442, 531405, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 81⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
      3. linear OA(81¹, 7, F₈₁, 1) (dual of [7, 6, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
2. linear OA(9⁸⁸, 1062899, F₉, 14) (dual of [1062899, 1062811, 15]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 9⁸⁸Â > V_b^sâˆ’1(kâˆ’1)Â = 195 096274 449505 849999 778866 197233 512863 310189 042254 841461 945377 633250 865364 810193 [i]
3. linear OA(9⁰, 1, F₉, 0) (dual of [1, 1, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
    - OA with only one run / dual of code without redundancy [i]

Mode: 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.