MinT - Information on Result #2637487

Information on Result #2637487

Linear OOA(4²⁴¹, 120, F₄, 3, 139) (dual of [(120, 3), 119, 140]-NRT-code), using strength reduction based on linear OOA(4²⁴¹, 120, F₄, 3, 140) (dual of [(120, 3), 119, 141]-NRT-code), using

constructionÂ X applied to AG(3;F,168P) âŠ‚ AG(3;F,192P) [i] based on
1. linear OOA(4²¹³, 103, F₄, 3, 140) (dual of [(103, 3), 96, 141]-NRT-code), using algebraic-geometric NRT-code AG(3;F,168P) [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(4¹⁸⁹, 103, F₄, 3, 116) (dual of [(103, 3), 120, 117]-NRT-code), using algebraic-geometric NRT-code AG(3;F,192P) [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104 (see above)
3. linear OOA(4²⁸, 17, F₄, 3, 23) (dual of [(17, 3), 23, 24]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,27P) [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, 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.