MinT - Information on Result #2634681

Information on Result #2634681

Linear OOA(4²⁰⁵, 77, F₄, 3, 138) (dual of [(77, 3), 26, 139]-NRT-code), using strength reduction based on linear OOA(4²⁰⁵, 77, F₄, 3, 139) (dual of [(77, 3), 26, 140]-NRT-code), using

constructionÂ X applied to AG(3;F,0P) âŠ‚ AG(3;F,58P) [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(4¹³⁹, 55, F₄, 3, 106) (dual of [(55, 3), 26, 107]-NRT-code), using algebraic-geometric NRT-code AG(3;F,58P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56 (see above)
3. linear OOA(4⁴¹, 22, F₄, 3, 32) (dual of [(22, 3), 25, 33]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,33P) [i] based on function field F/F₄ with g(F) = 9 and N(F) ≥ 22, 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.