MinT - Information on Result #974467

Information on Result #974467

Linear OOA(5¹³⁰, 130, F₅, 3, 50) (dual of [(130, 3), 260, 51]-NRT-code), using OOA 2-folding based on linear OOA(5¹³⁰, 260, F₅, 2, 50) (dual of [(260, 2), 390, 51]-NRT-code), using

trace code [i] based on linear OOA(25⁶⁵, 130, F₂₅, 2, 50) (dual of [(130, 2), 195, 51]-NRT-code), using
- constructionÂ X applied to AG(2;F,199P) âŠ‚ AG(2;F,205P) [i] based on
  1. linear OOA(25⁶⁰, 125, F₂₅, 2, 50) (dual of [(125, 2), 190, 51]-NRT-code), using algebraic-geometric NRT-code AG(2;F,199P) [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(25⁵⁴, 125, F₂₅, 2, 44) (dual of [(125, 2), 196, 45]-NRT-code), using algebraic-geometric NRT-code AG(2;F,205P) [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.