MinT - Information on Result #2663482

Information on Result #2663482

Linear OOA(4²¹⁰, 78, F₄, 3, 145) (dual of [(78, 3), 24, 146]-NRT-code), using 12 step truncation based on linear OOA(4²²², 82, F₄, 3, 157) (dual of [(82, 3), 24, 158]-NRT-code), using

constructionÂ X applied to AG(3;F,0P) âŠ‚ AG(3;F,56P) [i] based on
1. linear OOA(4¹⁶⁴, 55, F₄, 3, 164) (dual of [(55, 3), 1, 165]-NRT-code), using algebraic-geometric NRT-code AG(3;F,0P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
  - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
2. linear OOA(4¹⁴¹, 55, F₄, 3, 108) (dual of [(55, 3), 24, 109]-NRT-code), using algebraic-geometric NRT-code AG(3;F,56P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56 (see above)
3. linear OOA(4⁵⁸, 27, F₄, 3, 48) (dual of [(27, 3), 23, 49]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,32P) [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, 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.