MinT - Information on Result #2630729

Information on Result #2630729

Linear OOA(4¹¹³, 64, F₄, 3, 65) (dual of [(64, 3), 79, 66]-NRT-code), using strength reduction based on linear OOA(4¹¹³, 64, F₄, 3, 66) (dual of [(64, 3), 79, 67]-NRT-code), using

constructionÂ X applied to AG(3;F,98P) âŠ‚ AG(3;F,112P) [i] based on
1. linear OOA(4⁹⁹, 55, F₄, 3, 66) (dual of [(55, 3), 66, 67]-NRT-code), using algebraic-geometric NRT-code AG(3;F,98P) [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(4⁸⁵, 55, F₄, 3, 52) (dual of [(55, 3), 80, 53]-NRT-code), using algebraic-geometric NRT-code AG(3;F,112P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56 (see above)
3. linear OOA(4¹⁴, 9, F₄, 3, 13) (dual of [(9, 3), 13, 14]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,13P) [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.