MinT - Information on Result #2438661

Information on Result #2438661

Linear OOA(4⁵⁷, 41, F₄, 2, 32) (dual of [(41, 2), 25, 33]-NRT-code), using strength reduction based on linear OOA(4⁵⁷, 41, F₄, 2, 33) (dual of [(41, 2), 25, 34]-NRT-code), using

constructionÂ X applied to AG(2;F,30P) âŠ‚ AG(2;F,39P) [i] based on
1. linear OOA(4⁴⁸, 32, F₄, 2, 33) (dual of [(32, 2), 16, 34]-NRT-code), using algebraic-geometric NRT-code AG(2;F,30P) [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(4³⁹, 32, F₄, 2, 24) (dual of [(32, 2), 25, 25]-NRT-code), using algebraic-geometric NRT-code AG(2;F,39P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33 (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.