MinT - Information on Result #2630319

Information on Result #2630319

Linear OOA(4⁹⁹, 41, F₄, 3, 69) (dual of [(41, 3), 24, 70]-NRT-code), using strength reduction based on linear OOA(4⁹⁹, 41, F₄, 3, 70) (dual of [(41, 3), 24, 71]-NRT-code), using

constructionÂ X applied to AG(3;F,25P) âŠ‚ AG(3;F,39P) [i] based on
1. linear OOA(4⁸⁵, 32, F₄, 3, 70) (dual of [(32, 3), 11, 71]-NRT-code), using algebraic-geometric NRT-code AG(3;F,25P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
  - an explicitly constructive algebraic function field [i]
2. linear OOA(4⁷¹, 32, F₄, 3, 56) (dual of [(32, 3), 25, 57]-NRT-code), using algebraic-geometric NRT-code AG(3;F,39P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33 (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.