MinT - Information on Result #2838308

Information on Result #2838308

Linear OOA(2⁷⁹, 23, F₂, 5, 49) (dual of [(23, 5), 36, 50]-NRT-code), using strength reduction based on linear OOA(2⁷⁹, 23, F₂, 5, 50) (dual of [(23, 5), 36, 51]-NRT-code), using

constructionÂ X applied to AG(5;F,44P) âŠ‚ AG(5;F,54P) [i] based on
1. linear OOA(2⁶⁹, 19, F₂, 5, 50) (dual of [(19, 5), 26, 51]-NRT-code), using algebraic-geometric NRT-code AG(5;F,44P) [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(2⁵⁹, 19, F₂, 5, 40) (dual of [(19, 5), 36, 41]-NRT-code), using algebraic-geometric NRT-code AG(5;F,54P) [i] based on function field F/F₂ with g(F) = 19 and N(F) ≥ 20 (see above)
3. linear OOA(2¹⁰, 4, F₂, 5, 9) (dual of [(4, 5), 10, 10]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(2¹⁰, 5, F₂, 4, 9) (dual of [(5, 4), 10, 10]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,10P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, 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.