MinT - Information on Result #2505168

Information on Result #2505168

Linear OOA(5¹²⁷, 266, F₅, 2, 45) (dual of [(266, 2), 405, 46]-NRT-code), using 5¹ times duplication based on linear OOA(5¹²⁶, 266, F₅, 2, 45) (dual of [(266, 2), 406, 46]-NRT-code), using

trace code [i] based on linear OOA(25⁶³, 133, F₂₅, 2, 45) (dual of [(133, 2), 203, 46]-NRT-code), using
- constructionÂ X applied to AG(2;F,204P) âŠ‚ AG(2;F,213P) [i] based on
  1. linear OOA(25⁵⁵, 125, F₂₅, 2, 45) (dual of [(125, 2), 195, 46]-NRT-code), using algebraic-geometric NRT-code AG(2;F,204P) [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(25⁴⁶, 125, F₂₅, 2, 36) (dual of [(125, 2), 204, 37]-NRT-code), using algebraic-geometric NRT-code AG(2;F,213P) [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126 (see above)
  3. linear OOA(25⁸, 8, F₂₅, 2, 8) (dual of [(8, 2), 8, 9]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(25⁸, 25, F₂₅, 2, 8) (dual of [(25, 2), 42, 9]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;42,25) [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.