MinT - Information on Result #2636442

Information on Result #2636442

Linear OOA(4²²⁸, 145, F₄, 3, 96) (dual of [(145, 3), 207, 97]-NRT-code), using strength reduction based on linear OOA(4²²⁸, 145, F₄, 3, 97) (dual of [(145, 3), 207, 98]-NRT-code), using

constructionÂ X applied to AG(3;F,289P) âŠ‚ AG(3;F,311P) [i] based on
1. linear OOA(4²⁰², 129, F₄, 3, 97) (dual of [(129, 3), 185, 98]-NRT-code), using algebraic-geometric NRT-code AG(3;F,289P) [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(4¹⁸⁰, 129, F₄, 3, 75) (dual of [(129, 3), 207, 76]-NRT-code), using algebraic-geometric NRT-code AG(3;F,311P) [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130 (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.