MinT - Information on Result #2504924

Information on Result #2504924

Linear OOA(5¹⁰⁵, 256, F₅, 2, 39) (dual of [(256, 2), 407, 40]-NRT-code), using 5¹ times duplication based on linear OOA(5¹⁰⁴, 256, F₅, 2, 39) (dual of [(256, 2), 408, 40]-NRT-code), using

trace code [i] based on linear OOA(25⁵², 128, F₂₅, 2, 39) (dual of [(128, 2), 204, 40]-NRT-code), using
- constructionÂ X applied to AG(2;F,210P) âŠ‚ AG(2;F,214P) [i] based on
  1. linear OOA(25⁴⁹, 125, F₂₅, 2, 39) (dual of [(125, 2), 201, 40]-NRT-code), using algebraic-geometric NRT-code AG(2;F,210P) [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
    - the Hermitian function field over F₂₅ [i]
  2. linear OOA(25⁴⁵, 125, F₂₅, 2, 35) (dual of [(125, 2), 205, 36]-NRT-code), using algebraic-geometric NRT-code AG(2;F,214P) [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126 (see above)
  3. linear OOA(25³, 3, F₂₅, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(25³, 25, F₂₅, 2, 3) (dual of [(25, 2), 47, 4]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;47,25) [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.