MinT - Information on Result #1070862

Information on Result #1070862

Linear OOA(128⁷², 4192, F₁₂₈, 4, 28) (dual of [(4192, 4), 16696, 29]-NRT-code), using OOA 2-folding based on linear OOA(128⁷², 8384, F₁₂₈, 2, 28) (dual of [(8384, 2), 16696, 29]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(128⁷², 8385, F₁₂₈, 2, 28) (dual of [(8385, 2), 16698, 29]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(128¹⁷, 192, F₁₂₈, 2, 14) (dual of [(192, 2), 367, 15]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,369P) [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
      - a function field by SÃ©mirat [i]
  2. linear OOA(128⁵⁵, 8193, F₁₂₈, 2, 28) (dual of [(8193, 2), 16331, 29]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(128⁵⁵, 16386, F₁₂₈, 28) (dual of [16386, 16331, 29]-code), using
      - constructionÂ X applied to C_e(27) âŠ‚ C_e(26) [i] based on
        linear OA(128⁵⁵, 16384, F₁₂₈, 28) (dual of [16384, 16329, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
        linear OA(128⁵³, 16384, F₁₂₈, 27) (dual of [16384, 16331, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
        linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(128⁰, s, F₁₂₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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.