MinT - Information on Result #2758246

Information on Result #2758246

Linear OOA(2⁶⁹, 25, F₂, 4, 36) (dual of [(25, 4), 31, 37]-NRT-code), using strength reduction based on linear OOA(2⁶⁹, 25, F₂, 4, 37) (dual of [(25, 4), 31, 38]-NRT-code), using

constructionÂ X applied to AG(4;F,38P) âŠ‚ AG(4;F,50P) [i] based on
1. 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, using
  - an explicitly constructive algebraic function field [i]
2. linear OOA(2⁴⁴, 19, F₂, 4, 25) (dual of [(19, 4), 32, 26]-NRT-code), using algebraic-geometric NRT-code AG(4;F,50P) [i] based on function field F/F₂ with g(F) = 19 and N(F) ≥ 20 (see above)
3. linear OOA(2¹³, 6, F₂, 4, 11) (dual of [(6, 4), 11, 12]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,12P) [i] based on function field F/F₂ with g(F) = 2 and N(F) ≥ 6, 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.