MinT - Information on Result #973984

Information on Result #973984

Linear OOA(5¹⁰⁸, 130, F₅, 3, 39) (dual of [(130, 3), 282, 40]-NRT-code), using OOA 2-folding based on linear OOA(5¹⁰⁸, 260, F₅, 2, 39) (dual of [(260, 2), 412, 40]-NRT-code), using

trace code [i] based on linear OOA(25⁵⁴, 130, F₂₅, 2, 39) (dual of [(130, 2), 206, 40]-NRT-code), using
- constructionÂ X applied to AG(2;F,210P) âŠ‚ AG(2;F,216P) [i] based on
  1. linear OOA(25⁴⁹, 125, F₂₅, 2, 39) (dual of [(125, 2), 201, 40]-NRT-code), using algebraic-geometric NRT-code AG(2;F,210P) [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
    - the Hermitian function field over F₂₅ [i]
  2. linear OOA(25⁴³, 125, F₂₅, 2, 33) (dual of [(125, 2), 207, 34]-NRT-code), using algebraic-geometric NRT-code AG(2;F,216P) [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126 (see above)
  3. linear OOA(25⁵, 5, F₂₅, 2, 5) (dual of [(5, 2), 5, 6]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(25⁵, 25, F₂₅, 2, 5) (dual of [(25, 2), 45, 6]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;45,25) [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.