MinT - Information on Result #974578

Information on Result #974578

Linear OOA(5¹⁴⁰, 132, F₅, 3, 53) (dual of [(132, 3), 256, 54]-NRT-code), using OOA 2-folding based on linear OOA(5¹⁴⁰, 264, F₅, 2, 53) (dual of [(264, 2), 388, 54]-NRT-code), using

trace code [i] based on linear OOA(25⁷⁰, 132, F₂₅, 2, 53) (dual of [(132, 2), 194, 54]-NRT-code), using
- constructionÂ X applied to AG(2;F,196P) âŠ‚ AG(2;F,204P) [i] based on
  1. linear OOA(25⁶³, 125, F₂₅, 2, 53) (dual of [(125, 2), 187, 54]-NRT-code), using algebraic-geometric NRT-code AG(2;F,196P) [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(25⁵⁵, 125, F₂₅, 2, 45) (dual of [(125, 2), 195, 46]-NRT-code), using algebraic-geometric NRT-code AG(2;F,204P) [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126 (see above)
  3. linear OOA(25⁷, 7, F₂₅, 2, 7) (dual of [(7, 2), 7, 8]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(25⁷, 25, F₂₅, 2, 7) (dual of [(25, 2), 43, 8]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;43,25) [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.