MinT - Information on Result #2643421

Information on Result #2643421

Linear OOA(8⁷⁸, 74, F₈, 3, 48) (dual of [(74, 3), 144, 49]-NRT-code), using strength reduction based on linear OOA(8⁷⁸, 74, F₈, 3, 49) (dual of [(74, 3), 144, 50]-NRT-code), using

constructionÂ X applied to AG(3;F,142P) âŠ‚ AG(3;F,157P) [i] based on
1. linear OOA(8⁶³, 64, F₈, 3, 49) (dual of [(64, 3), 129, 50]-NRT-code), using algebraic-geometric NRT-code AG(3;F,142P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
  - the Suzuki function field over F₈ [i]
2. linear OOA(8⁴⁸, 64, F₈, 3, 34) (dual of [(64, 3), 144, 35]-NRT-code), using algebraic-geometric NRT-code AG(3;F,157P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
3. linear OOA(8¹⁵, 10, F₈, 3, 14) (dual of [(10, 3), 15, 15]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8¹⁵, 14, F₈, 3, 14) (dual of [(14, 3), 27, 15]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,27P) [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
      - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [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.