MinT - Information on Result #1134058

Information on Result #1134058

Linear OOA(2¹⁷⁰, 58, F₂, 6, 48) (dual of [(58, 6), 178, 49]-NRT-code), using OOA 2-folding based on linear OOA(2¹⁷⁰, 116, F₂, 3, 48) (dual of [(116, 3), 178, 49]-NRT-code), using

trace code [i] based on linear OOA(4⁸⁵, 58, F₄, 3, 48) (dual of [(58, 3), 89, 49]-NRT-code), using
- constructionÂ X applied to AG(3;F,116P) âŠ‚ AG(3;F,121P) [i] based on
  1. linear OOA(4⁸¹, 55, F₄, 3, 48) (dual of [(55, 3), 84, 49]-NRT-code), using algebraic-geometric NRT-code AG(3;F,116P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
  2. linear OOA(4⁷⁶, 55, F₄, 3, 43) (dual of [(55, 3), 89, 44]-NRT-code), using algebraic-geometric NRT-code AG(3;F,121P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56 (see above)
  3. linear OOA(4⁴, 3, F₄, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4⁴, 4, F₄, 3, 4) (dual of [(4, 3), 8, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;8,4) [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.