MinT - Information on Result #2758786

Information on Result #2758786

Linear OOA(2⁸⁹, 27, F₂, 4, 51) (dual of [(27, 4), 19, 52]-NRT-code), using strength reduction based on linear OOA(2⁸⁹, 27, F₂, 4, 52) (dual of [(27, 4), 19, 53]-NRT-code), using

constructionÂ X applied to AG(4;F,23P) âŠ‚ AG(4;F,38P) [i] based on
1. linear OOA(2⁷¹, 19, F₂, 4, 52) (dual of [(19, 4), 5, 53]-NRT-code), using algebraic-geometric NRT-code AG(4;F,23P) [i] based on function field F/F₂ with g(F) = 19 and N(F) ≥ 20, using
  - an explicitly constructive algebraic function field [i]
2. linear OOA(2⁵⁶, 19, F₂, 4, 37) (dual of [(19, 4), 20, 38]-NRT-code), using algebraic-geometric NRT-code AG(4;F,38P) [i] based on function field F/F₂ with g(F) = 19 and N(F) ≥ 20 (see above)
3. linear OOA(2¹⁸, 8, F₂, 4, 14) (dual of [(8, 4), 14, 15]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,17P) [i] based on function field F/F₂ with g(F) = 4 and N(F) ≥ 8, 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.