MinT - Information on Result #2278181

Information on Result #2278181

Linear OA(5¹⁴⁵, 257, F₅, 61) (dual of [257, 112, 62]-code), using 1 times code embedding in larger space based on linear OA(5¹⁴⁴, 256, F₅, 61) (dual of [256, 112, 62]-code), using

trace code [i] based on linear OA(25⁷², 128, F₂₅, 61) (dual of [128, 56, 62]-code), using
- constructionÂ X applied to AG(F,63P) âŠ‚ AG(F,65P) [i] based on
  1. linear OA(25⁷¹, 125, F₂₅, 61) (dual of [125, 54, 62]-code), using algebraic-geometric code AG(F,63P) [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 OA(25⁶⁹, 125, F₂₅, 59) (dual of [125, 56, 60]-code), using algebraic-geometric code AG(F,65P) [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126 (see above)
  3. linear OA(25¹, 3, F₂₅, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(25¹, s, F₂₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [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.