MinT - Information on Result #2637145

Information on Result #2637145

Linear OOA(4²³⁷, 112, F₄, 3, 149) (dual of [(112, 3), 99, 150]-NRT-code), using strength reduction based on linear OOA(4²³⁷, 112, F₄, 3, 150) (dual of [(112, 3), 99, 151]-NRT-code), using

constructionÂ X applied to AG(3;F,158P) âŠ‚ AG(3;F,172P) [i] based on
1. linear OOA(4²²³, 103, F₄, 3, 150) (dual of [(103, 3), 86, 151]-NRT-code), using algebraic-geometric NRT-code AG(3;F,158P) [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(4²⁰⁹, 103, F₄, 3, 136) (dual of [(103, 3), 100, 137]-NRT-code), using algebraic-geometric NRT-code AG(3;F,172P) [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104 (see above)
3. linear OOA(4¹⁴, 9, F₄, 3, 13) (dual of [(9, 3), 13, 14]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,13P) [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.