MinT - Information on Result #2630299

Information on Result #2630299

Linear OOA(4⁹⁸, 63, F₄, 3, 52) (dual of [(63, 3), 91, 53]-NRT-code), using strength reduction based on linear OOA(4⁹⁸, 63, F₄, 3, 53) (dual of [(63, 3), 91, 54]-NRT-code), using

constructionÂ X applied to AG(3;F,111P) âŠ‚ AG(3;F,123P) [i] based on
1. linear OOA(4⁸⁶, 55, F₄, 3, 53) (dual of [(55, 3), 79, 54]-NRT-code), using algebraic-geometric NRT-code AG(3;F,111P) [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(4⁷⁴, 55, F₄, 3, 41) (dual of [(55, 3), 91, 42]-NRT-code), using algebraic-geometric NRT-code AG(3;F,123P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56 (see above)
3. linear OOA(4¹², 8, F₄, 3, 11) (dual of [(8, 3), 12, 12]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4¹², 9, F₄, 3, 11) (dual of [(9, 3), 15, 12]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,15P) [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.