MinT - Information on Result #982403

Information on Result #982403

Linear OOA(8¹²³, 58, F₈, 3, 66) (dual of [(58, 3), 51, 67]-NRT-code), using OOA 2-folding based on linear OOA(8¹²³, 116, F₈, 2, 66) (dual of [(116, 2), 109, 67]-NRT-code), using

constructionÂ X applied to AG(2;F,127P) âŠ‚ AG(2;F,145P) [i] based on
1. linear OOA(8¹⁰³, 97, F₈, 2, 66) (dual of [(97, 2), 91, 67]-NRT-code), using algebraic-geometric NRT-code AG(2;F,127P) [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
  - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]
2. linear OOA(8⁸⁵, 97, F₈, 2, 48) (dual of [(97, 2), 109, 49]-NRT-code), using algebraic-geometric NRT-code AG(2;F,145P) [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98 (see above)
3. linear OOA(8²⁰, 19, F₈, 2, 17) (dual of [(19, 2), 18, 18]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8²⁰, 24, F₈, 2, 17) (dual of [(24, 2), 28, 18]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,30P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
      - the Klein quartic over F₈ [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.