MinT - Information on Result #2770356

Information on Result #2770356

Linear OOA(3¹²⁹, 50, F₃, 4, 77) (dual of [(50, 4), 71, 78]-NRT-code), using strength reduction based on linear OOA(3¹²⁹, 50, F₃, 4, 78) (dual of [(50, 4), 71, 79]-NRT-code), using

constructionÂ X applied to AG(4;F,109P) âŠ‚ AG(4;F,116P) [i] based on
1. linear OOA(3¹²³, 47, F₃, 4, 78) (dual of [(47, 4), 65, 79]-NRT-code), using algebraic-geometric NRT-code AG(4;F,109P) [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
  - an explicitly constructive algebraic function field [i]
2. linear OOA(3¹¹⁶, 47, F₃, 4, 71) (dual of [(47, 4), 72, 72]-NRT-code), using algebraic-geometric NRT-code AG(4;F,116P) [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48 (see above)
3. linear OOA(3⁶, 3, F₃, 4, 6) (dual of [(3, 4), 6, 7]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(4;6,3) [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.