MinT - Information on Result #2645917

Information on Result #2645917

Linear OOA(8¹⁶⁴, 117, F₈, 3, 95) (dual of [(117, 3), 187, 96]-NRT-code), using strength reduction based on linear OOA(8¹⁶⁴, 117, F₈, 3, 96) (dual of [(117, 3), 187, 97]-NRT-code), using

constructionÂ X applied to AG(3;F,194P) âŠ‚ AG(3;F,223P) [i] based on
1. linear OOA(8¹³³, 97, F₈, 3, 96) (dual of [(97, 3), 158, 97]-NRT-code), using algebraic-geometric NRT-code AG(3;F,194P) [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(8¹⁰⁴, 97, F₈, 3, 67) (dual of [(97, 3), 187, 68]-NRT-code), using algebraic-geometric NRT-code AG(3;F,223P) [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98 (see above)
3. linear OOA(8³¹, 20, F₈, 3, 28) (dual of [(20, 3), 29, 29]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8³¹, 24, F₈, 3, 28) (dual of [(24, 3), 41, 29]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,43P) [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.