MinT - Information on Result #981409

Information on Result #981409

Linear OOA(8⁶⁹, 37, F₈, 3, 45) (dual of [(37, 3), 42, 46]-NRT-code), using OOA 2-folding based on linear OOA(8⁶⁹, 74, F₈, 2, 45) (dual of [(74, 2), 79, 46]-NRT-code), using

constructionÂ X applied to AG(2;F,82P) âŠ‚ AG(2;F,92P) [i] based on
1. linear OOA(8⁵⁹, 64, F₈, 2, 45) (dual of [(64, 2), 69, 46]-NRT-code), using algebraic-geometric NRT-code AG(2;F,82P) [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(8⁴⁹, 64, F₈, 2, 35) (dual of [(64, 2), 79, 36]-NRT-code), using algebraic-geometric NRT-code AG(2;F,92P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
3. linear OOA(8¹⁰, 10, F₈, 2, 9) (dual of [(10, 2), 10, 10]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8¹⁰, 14, F₈, 2, 9) (dual of [(14, 2), 18, 10]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,18P) [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.