MinT - Information on Result #2636821

Information on Result #2636821

Linear OOA(4²³³, 144, F₄, 3, 103) (dual of [(144, 3), 199, 104]-NRT-code), using strength reduction based on linear OOA(4²³³, 144, F₄, 3, 104) (dual of [(144, 3), 199, 105]-NRT-code), using

constructionÂ X applied to AG(3;F,282P) âŠ‚ AG(3;F,303P) [i] based on
1. linear OOA(4²⁰⁹, 129, F₄, 3, 104) (dual of [(129, 3), 178, 105]-NRT-code), using algebraic-geometric NRT-code AG(3;F,282P) [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
  - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
2. linear OOA(4¹⁸⁸, 129, F₄, 3, 83) (dual of [(129, 3), 199, 84]-NRT-code), using algebraic-geometric NRT-code AG(3;F,303P) [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130 (see above)
3. linear OOA(4²⁴, 15, F₄, 3, 20) (dual of [(15, 3), 21, 21]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,24P) [i] based on function field F/F₄ with g(F) = 4 and N(F) ≥ 15, using
    - an explicitly constructive algebraic function field [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.