MinT - Information on Result #2630912

Information on Result #2630912

Linear OOA(4¹¹⁹, 73, F₄, 3, 57) (dual of [(73, 3), 100, 58]-NRT-code), using strength reduction based on linear OOA(4¹¹⁹, 73, F₄, 3, 58) (dual of [(73, 3), 100, 59]-NRT-code), using

constructionÂ X applied to AG(3;F,136P) âŠ‚ AG(3;F,148P) [i] based on
1. linear OOA(4¹⁰⁷, 65, F₄, 3, 58) (dual of [(65, 3), 88, 59]-NRT-code), using algebraic-geometric NRT-code AG(3;F,136P) [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
  - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
2. linear OOA(4⁹⁵, 65, F₄, 3, 46) (dual of [(65, 3), 100, 47]-NRT-code), using algebraic-geometric NRT-code AG(3;F,148P) [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66 (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.