MinT - Information on Result #2769459

Information on Result #2769459

Linear OOA(3⁹⁷, 44, F₃, 4, 53) (dual of [(44, 4), 79, 54]-NRT-code), using strength reduction based on linear OOA(3⁹⁷, 44, F₃, 4, 54) (dual of [(44, 4), 79, 55]-NRT-code), using

constructionÂ X applied to AG(4;F,44P) âŠ‚ AG(4;F,52P) [i] based on
1. linear OOA(3⁸¹, 36, F₃, 4, 55) (dual of [(36, 4), 63, 56]-NRT-code), using algebraic-geometric NRT-code AG(4;F,44P) 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(3⁶⁵, 36, F₃, 4, 39) (dual of [(36, 4), 79, 40]-NRT-code), using algebraic-geometric NRT-code AG(4;F,52P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
3. linear OOA(3¹⁶, 8, F₃, 4, 14) (dual of [(8, 4), 16, 15]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,17P) [i] based on function field F/F₃ with g(F) = 2 and N(F) ≥ 8, using
    - an explicitly constructive algebraic function field [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.