MinT - Information on Result #1019421

Information on Result #1019421

Linear OOA(128⁵¹, 5783, F₁₂₈, 3, 18) (dual of [(5783, 3), 17298, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(128¹⁶, 321, F₁₂₈, 3, 9) (dual of [(321, 3), 947, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(128⁴, 129, F₁₂₈, 3, 4) (dual of [(129, 3), 383, 5]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;383,128) [i]
  2. linear OOA(128¹², 192, F₁₂₈, 3, 9) (dual of [(192, 3), 564, 10]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,566P) [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(128³⁵, 5462, F₁₂₈, 3, 18) (dual of [(5462, 3), 16351, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(128³⁵, 16386, F₁₂₈, 18) (dual of [16386, 16351, 19]-code), using
  - constructionÂ X applied to C_e(17) âŠ‚ C_e(16) [i] based on
    1. linear OA(128³⁵, 16384, F₁₂₈, 18) (dual of [16384, 16349, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
    2. linear OA(128³³, 16384, F₁₂₈, 17) (dual of [16384, 16351, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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.