MinT - Information on Result #2663500

Information on Result #2663500

Linear OOA(4²¹⁶, 81, F₄, 3, 148) (dual of [(81, 3), 27, 149]-NRT-code), using 3 step truncation based on linear OOA(4²¹⁹, 82, F₄, 3, 151) (dual of [(82, 3), 27, 152]-NRT-code), using

constructionÂ X applied to AG(3;F,0P) âŠ‚ AG(3;F,59P) [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(4¹³⁸, 55, F₄, 3, 105) (dual of [(55, 3), 27, 106]-NRT-code), using algebraic-geometric NRT-code AG(3;F,59P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56 (see above)
3. linear OOA(4⁵⁵, 27, F₄, 3, 45) (dual of [(27, 3), 26, 46]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,35P) [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.