MinT - Information on Result #2497825

Information on Result #2497825

Linear OOA(4⁸⁵, 65, F₄, 2, 41) (dual of [(65, 2), 45, 42]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4⁸³, 64, F₄, 2, 41) (dual of [(64, 2), 45, 42]-NRT-code), using

constructionÂ X applied to AG(2;F,68P) âŠ‚ AG(2;F,77P) [i] based on
1. linear OOA(4⁷⁴, 55, F₄, 2, 41) (dual of [(55, 2), 36, 42]-NRT-code), using algebraic-geometric NRT-code AG(2;F,68P) [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(4⁶⁵, 55, F₄, 2, 32) (dual of [(55, 2), 45, 33]-NRT-code), using algebraic-geometric NRT-code AG(2;F,77P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56 (see above)
3. linear OOA(4⁹, 9, F₄, 2, 8) (dual of [(9, 2), 9, 9]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,9P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
    - the Hermitian function field over F₄ [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.