MinT - Information on Result #2505681

Information on Result #2505681

Linear OOA(5¹⁴¹, 136, F₅, 2, 63) (dual of [(136, 2), 131, 64]-NRT-code), using 5¹ times duplication based on linear OOA(5¹⁴⁰, 136, F₅, 2, 63) (dual of [(136, 2), 132, 64]-NRT-code), using

trace code [i] based on linear OOA(25⁷⁰, 68, F₂₅, 2, 63) (dual of [(68, 2), 66, 64]-NRT-code), using
- constructionÂ X applied to AG(2;F,66P) âŠ‚ AG(2;F,70P) [i] based on
  1. linear OOA(25⁶⁷, 65, F₂₅, 2, 63) (dual of [(65, 2), 63, 64]-NRT-code), using algebraic-geometric NRT-code AG(2;F,66P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OOA(25⁶³, 65, F₂₅, 2, 59) (dual of [(65, 2), 67, 60]-NRT-code), using algebraic-geometric NRT-code AG(2;F,70P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66 (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.