MinT - Information on Result #1019623

Information on Result #1019623

Linear OOA(128⁷⁷, 5807, F₁₂₈, 3, 27) (dual of [(5807, 3), 17344, 28]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(128²⁴, 345, F₁₂₈, 3, 13) (dual of [(345, 3), 1011, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(128⁶, 129, F₁₂₈, 3, 6) (dual of [(129, 3), 381, 7]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;381,128) [i]
  2. linear OOA(128¹⁸, 216, F₁₂₈, 3, 13) (dual of [(216, 3), 630, 14]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,634P) [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
      - a function field by SÃ©mirat [i]
linear OOA(128⁵³, 5462, F₁₂₈, 3, 27) (dual of [(5462, 3), 16333, 28]-NRT-code), using
- OOA 3-folding [i] based on linear OA(128⁵³, 16386, F₁₂₈, 27) (dual of [16386, 16333, 28]-code), using
  - constructionÂ X applied to C_e(26) âŠ‚ C_e(25) [i] based on
    1. 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]
    2. linear OA(128⁵¹, 16384, F₁₂₈, 26) (dual of [16384, 16333, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [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.