MinT - Information on Result #1070928

Information on Result #1070928

Linear OOA(128⁷⁷, 4192, F₁₂₈, 4, 30) (dual of [(4192, 4), 16691, 31]-NRT-code), using OOA 2-folding based on linear OOA(128⁷⁷, 8384, F₁₂₈, 2, 30) (dual of [(8384, 2), 16691, 31]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(128⁷⁷, 8385, F₁₂₈, 2, 30) (dual of [(8385, 2), 16693, 31]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(128¹⁸, 192, F₁₂₈, 2, 15) (dual of [(192, 2), 366, 16]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,368P) [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(128⁵⁹, 8193, F₁₂₈, 2, 30) (dual of [(8193, 2), 16327, 31]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(128⁵⁹, 16386, F₁₂₈, 30) (dual of [16386, 16327, 31]-code), using
      - constructionÂ X applied to C_e(29) âŠ‚ C_e(28) [i] based on
        linear OA(128⁵⁹, 16384, F₁₂₈, 30) (dual of [16384, 16325, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
        linear OA(128⁵⁷, 16384, F₁₂₈, 29) (dual of [16384, 16327, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [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.