MinT - Information on Result #982149

Information on Result #982149

Linear OOA(8⁸⁴, 37, F₈, 3, 60) (dual of [(37, 3), 27, 61]-NRT-code), using OOA 2-folding based on linear OOA(8⁸⁴, 74, F₈, 2, 60) (dual of [(74, 2), 64, 61]-NRT-code), using

constructionÂ X applied to AG(2;F,67P) âŠ‚ AG(2;F,77P) [i] based on
1. linear OOA(8⁷⁴, 64, F₈, 2, 60) (dual of [(64, 2), 54, 61]-NRT-code), using algebraic-geometric NRT-code AG(2;F,67P) [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(8⁶⁴, 64, F₈, 2, 50) (dual of [(64, 2), 64, 51]-NRT-code), using algebraic-geometric NRT-code AG(2;F,77P) [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.