MinT - Information on Result #905136

Information on Result #905136

Linear OOA(128⁵⁹, 8514, F₁₂₈, 2, 21) (dual of [(8514, 2), 16969, 22]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(128¹⁸, 321, F₁₂₈, 2, 10) (dual of [(321, 2), 624, 11]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(128⁵, 129, F₁₂₈, 2, 5) (dual of [(129, 2), 253, 6]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;253,128) [i]
  2. linear OOA(128¹³, 192, F₁₂₈, 2, 10) (dual of [(192, 2), 371, 11]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,373P) [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
      - a function field by SÃ©mirat [i]
linear OOA(128⁴¹, 8193, F₁₂₈, 2, 21) (dual of [(8193, 2), 16345, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128⁴¹, 16386, F₁₂₈, 21) (dual of [16386, 16345, 22]-code), using
  - constructionÂ X applied to C_e(20) âŠ‚ C_e(19) [i] based on
    1. linear OA(128⁴¹, 16384, F₁₂₈, 21) (dual of [16384, 16343, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
    2. linear OA(128³⁹, 16384, F₁₂₈, 20) (dual of [16384, 16345, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
    3. 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.