MinT - Information on Result #2630877

Information on Result #2630877

Linear OOA(4¹¹⁸, 61, F₄, 3, 75) (dual of [(61, 3), 65, 76]-NRT-code), using strength reduction based on linear OOA(4¹¹⁸, 61, F₄, 3, 76) (dual of [(61, 3), 65, 77]-NRT-code), using

constructionÂ X applied to AG(3;F,88P) âŠ‚ AG(3;F,97P) [i] based on
1. linear OOA(4¹⁰⁹, 55, F₄, 3, 76) (dual of [(55, 3), 56, 77]-NRT-code), using algebraic-geometric NRT-code AG(3;F,88P) [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(4¹⁰⁰, 55, F₄, 3, 67) (dual of [(55, 3), 65, 68]-NRT-code), using algebraic-geometric NRT-code AG(3;F,97P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56 (see above)
3. linear OOA(4⁹, 6, F₄, 3, 8) (dual of [(6, 3), 9, 9]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4⁹, 9, F₄, 3, 8) (dual of [(9, 3), 18, 9]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,18P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
      - the Hermitian function field over F₄ [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.