MinT - Information on Result #2721604

Information on Result #2721604

Linear OOA(8¹⁷², 157, F₈, 3, 105) (dual of [(157, 3), 299, 106]-NRT-code), using strength reduction based on linear OOA(8¹⁷², 157, F₈, 3, 106) (dual of [(157, 3), 299, 107]-NRT-code), using

constructionÂ X applied to AG(3;F,322P) âŠ‚ AG(3;F,343P) [i] based on
1. linear OOA(8¹⁵¹, 143, F₈, 3, 106) (dual of [(143, 3), 278, 107]-NRT-code), using algebraic-geometric NRT-code AG(3;F,322P) [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(8¹³⁰, 143, F₈, 3, 85) (dual of [(143, 3), 299, 86]-NRT-code), using algebraic-geometric NRT-code AG(3;F,343P) [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144 (see above)
3. linear OOA(8²¹, 14, F₈, 3, 20) (dual of [(14, 3), 21, 21]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,21P) [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.