MinT - Information on Result #2720962

Information on Result #2720962

Linear OOA(8¹³⁸, 153, F₈, 3, 77) (dual of [(153, 3), 321, 78]-NRT-code), using strength reduction based on linear OOA(8¹³⁸, 153, F₈, 3, 78) (dual of [(153, 3), 321, 79]-NRT-code), using

constructionÂ X applied to AG(3;F,350P) âŠ‚ AG(3;F,365P) [i] based on
1. linear OOA(8¹²³, 143, F₈, 3, 78) (dual of [(143, 3), 306, 79]-NRT-code), using algebraic-geometric NRT-code AG(3;F,350P) [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
  - Drinfeld modules of rank 1 [i]
2. linear OOA(8¹⁰⁸, 143, F₈, 3, 63) (dual of [(143, 3), 321, 64]-NRT-code), using algebraic-geometric NRT-code AG(3;F,365P) [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144 (see above)
3. linear OOA(8¹⁵, 10, F₈, 3, 14) (dual of [(10, 3), 15, 15]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8¹⁵, 14, F₈, 3, 14) (dual of [(14, 3), 27, 15]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,27P) [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: 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.