MinT - Information on Result #1019366

Information on Result #1019366

Linear OOA(128⁴⁴, 5741, F₁₂₈, 3, 16) (dual of [(5741, 3), 17179, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(128¹³, 279, F₁₂₈, 3, 8) (dual of [(279, 3), 824, 9]-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(128⁹, 150, F₁₂₈, 3, 8) (dual of [(150, 3), 441, 9]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,441P) [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]
linear OOA(128³¹, 5462, F₁₂₈, 3, 16) (dual of [(5462, 3), 16355, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(128³¹, 16386, F₁₂₈, 16) (dual of [16386, 16355, 17]-code), using
  - constructionÂ X applied to C_e(15) âŠ‚ C_e(14) [i] based on
    1. linear OA(128³¹, 16384, F₁₂₈, 16) (dual of [16384, 16353, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
    2. linear OA(128²⁹, 16384, F₁₂₈, 15) (dual of [16384, 16355, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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.