MinT - Information on Result #2635290

Information on Result #2635290

Linear OOA(4²¹³, 119, F₄, 3, 113) (dual of [(119, 3), 144, 114]-NRT-code), using strength reduction based on linear OOA(4²¹³, 119, F₄, 3, 114) (dual of [(119, 3), 144, 115]-NRT-code), using

constructionÂ X applied to AG(3;F,194P) âŠ‚ AG(3;F,216P) [i] based on
1. linear OOA(4¹⁸⁷, 103, F₄, 3, 114) (dual of [(103, 3), 122, 115]-NRT-code), using algebraic-geometric NRT-code AG(3;F,194P) [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(4¹⁶⁵, 103, F₄, 3, 92) (dual of [(103, 3), 144, 93]-NRT-code), using algebraic-geometric NRT-code AG(3;F,216P) [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104 (see above)
3. linear OOA(4²⁶, 16, F₄, 3, 21) (dual of [(16, 3), 22, 22]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4²⁶, 17, F₄, 3, 21) (dual of [(17, 3), 25, 22]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,29P) [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.