MinT - Information on Result #2644676

Information on Result #2644676

Linear OOA(8¹²⁹, 109, F₈, 3, 73) (dual of [(109, 3), 198, 74]-NRT-code), using strength reduction based on linear OOA(8¹²⁹, 109, F₈, 3, 74) (dual of [(109, 3), 198, 75]-NRT-code), using

constructionÂ X applied to AG(3;F,216P) âŠ‚ AG(3;F,234P) [i] based on
1. linear OOA(8¹¹¹, 97, F₈, 3, 74) (dual of [(97, 3), 180, 75]-NRT-code), using algebraic-geometric NRT-code AG(3;F,216P) [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(8⁹³, 97, F₈, 3, 56) (dual of [(97, 3), 198, 57]-NRT-code), using algebraic-geometric NRT-code AG(3;F,234P) [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98 (see above)
3. linear OOA(8¹⁸, 12, F₈, 3, 17) (dual of [(12, 3), 18, 18]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8¹⁸, 14, F₈, 3, 17) (dual of [(14, 3), 24, 18]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,24P) [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.