MinT - Information on Result #2278124

Information on Result #2278124

Linear OA(5¹³⁷, 257, F₅, 57) (dual of [257, 120, 58]-code), using 1 times code embedding in larger space based on linear OA(5¹³⁶, 256, F₅, 57) (dual of [256, 120, 58]-code), using

trace code [i] based on linear OA(25⁶⁸, 128, F₂₅, 57) (dual of [128, 60, 58]-code), using
- constructionÂ X applied to AG(F,67P) âŠ‚ AG(F,69P) [i] based on
  1. linear OA(25⁶⁷, 125, F₂₅, 57) (dual of [125, 58, 58]-code), using algebraic-geometric code AG(F,67P) [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(25⁶⁵, 125, F₂₅, 55) (dual of [125, 60, 56]-code), using algebraic-geometric code AG(F,69P) [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.