MinT - Information on Result #2505314

Information on Result #2505314

Linear OOA(5¹²⁷, 258, F₅, 2, 49) (dual of [(258, 2), 389, 50]-NRT-code), using 5¹ times duplication based on linear OOA(5¹²⁶, 258, F₅, 2, 49) (dual of [(258, 2), 390, 50]-NRT-code), using

trace code [i] based on linear OOA(25⁶³, 129, F₂₅, 2, 49) (dual of [(129, 2), 195, 50]-NRT-code), using
- constructionÂ X applied to AG(2;F,200P) âŠ‚ AG(2;F,205P) [i] based on
  1. linear OOA(25⁵⁹, 125, F₂₅, 2, 49) (dual of [(125, 2), 191, 50]-NRT-code), using algebraic-geometric NRT-code AG(2;F,200P) [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(25⁵⁴, 125, F₂₅, 2, 44) (dual of [(125, 2), 196, 45]-NRT-code), using algebraic-geometric NRT-code AG(2;F,205P) [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126 (see above)
  3. linear OOA(25⁴, 4, F₂₅, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(25⁴, 25, F₂₅, 2, 4) (dual of [(25, 2), 46, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;46,25) [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.