MinT - Information on Result #2776559

Information on Result #2776559

Linear OOA(3²³⁵, 70, F₃, 4, 138) (dual of [(70, 4), 45, 139]-NRT-code), using strength reduction based on linear OOA(3²³⁵, 70, F₃, 4, 140) (dual of [(70, 4), 45, 141]-NRT-code), using

constructionÂ X applied to AG(4;F,0P) âŠ‚ AG(4;F,35P) [i] based on
1. linear OOA(3¹⁴³, 36, F₃, 4, 143) (dual of [(36, 4), 1, 144]-NRT-code), using algebraic-geometric NRT-code AG(4;F,0P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
2. linear OOA(3⁹⁹, 36, F₃, 4, 73) (dual of [(36, 4), 45, 74]-NRT-code), using algebraic-geometric NRT-code AG(4;F,35P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
3. linear OOA(3⁹², 34, F₃, 4, 66) (dual of [(34, 4), 44, 67]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3⁹², 35, F₃, 4, 66) (dual of [(35, 4), 48, 67]-NRT-code), using
    - algebraic-geometric NRT-code AG(4;F,73P) [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)

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.