MinT - Information on Result #2638340

Information on Result #2638340

Linear OOA(4²⁵¹, 109, F₄, 3, 168) (dual of [(109, 3), 76, 169]-NRT-code), using strength reduction based on linear OOA(4²⁵¹, 109, F₄, 3, 169) (dual of [(109, 3), 76, 170]-NRT-code), using

constructionÂ X applied to AG(3;F,139P) âŠ‚ AG(3;F,148P) [i] based on
1. linear OOA(4²⁴², 103, F₄, 3, 169) (dual of [(103, 3), 67, 170]-NRT-code), using algebraic-geometric NRT-code AG(3;F,139P) [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
  - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
2. linear OOA(4²³³, 103, F₄, 3, 160) (dual of [(103, 3), 76, 161]-NRT-code), using algebraic-geometric NRT-code AG(3;F,148P) [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104 (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.