MinT - Information on Result #1019466

Information on Result #1019466

Linear OOA(128⁵⁷, 5783, F₁₂₈, 3, 20) (dual of [(5783, 3), 17292, 21]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(128¹⁸, 321, F₁₂₈, 3, 10) (dual of [(321, 3), 945, 11]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(128⁵, 129, F₁₂₈, 3, 5) (dual of [(129, 3), 382, 6]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;382,128) [i]
  2. linear OOA(128¹³, 192, F₁₂₈, 3, 10) (dual of [(192, 3), 563, 11]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,565P) [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(128³⁹, 5462, F₁₂₈, 3, 20) (dual of [(5462, 3), 16347, 21]-NRT-code), using
- OOA 3-folding [i] based on linear OA(128³⁹, 16386, F₁₂₈, 20) (dual of [16386, 16347, 21]-code), using
  - constructionÂ X applied to C_e(19) âŠ‚ C_e(18) [i] based on
    1. 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]
    2. linear OA(128³⁷, 16384, F₁₂₈, 19) (dual of [16384, 16347, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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.