MinT - Information on Result #2663430

Information on Result #2663430

Linear OOA(4²⁰⁴, 75, F₄, 3, 145) (dual of [(75, 3), 21, 146]-NRT-code), using 3 step truncation based on linear OOA(4²⁰⁷, 76, F₄, 3, 148) (dual of [(76, 3), 21, 149]-NRT-code), using

constructionÂ X applied to AG(3;F,0P) âŠ‚ AG(3;F,53P) [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(4¹⁴⁴, 55, F₄, 3, 111) (dual of [(55, 3), 21, 112]-NRT-code), using algebraic-geometric NRT-code AG(3;F,53P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56 (see above)
3. linear OOA(4⁴³, 21, F₄, 3, 36) (dual of [(21, 3), 20, 37]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,26P) [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, 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.