MinT - Information on Result #2635751

Information on Result #2635751

Linear OOA(4²¹⁹, 145, F₄, 3, 87) (dual of [(145, 3), 216, 88]-NRT-code), using strength reduction based on linear OOA(4²¹⁹, 145, F₄, 3, 88) (dual of [(145, 3), 216, 89]-NRT-code), using

constructionÂ X applied to AG(3;F,298P) âŠ‚ AG(3;F,320P) [i] based on
1. linear OOA(4¹⁹³, 129, F₄, 3, 88) (dual of [(129, 3), 194, 89]-NRT-code), using algebraic-geometric NRT-code AG(3;F,298P) [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(4¹⁷¹, 129, F₄, 3, 66) (dual of [(129, 3), 216, 67]-NRT-code), using algebraic-geometric NRT-code AG(3;F,320P) [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.