MinT - Information on Result #2278217

Information on Result #2278217

Linear OA(5¹⁴⁷, 211, F₅, 64) (dual of [211, 64, 65]-code), using 2 times code embedding in larger space based on linear OA(5¹⁴⁵, 209, F₅, 64) (dual of [209, 64, 65]-code), using

1 times truncation [i] based on linear OA(5¹⁴⁶, 210, F₅, 65) (dual of [210, 64, 66]-code), using
- concatenation of two codes [i] based on
  1. linear OA(25³⁸, 70, F₂₅, 32) (dual of [70, 32, 33]-code), using
    - constructionÂ X applied to AG(F,32P) âŠ‚ AG(F,35P) [i] based on
      1. linear OA(25³⁶, 65, F₂₅, 32) (dual of [65, 29, 33]-code), using algebraic-geometric code AG(F,32P) [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 OA(25³³, 65, F₂₅, 29) (dual of [65, 32, 30]-code), using algebraic-geometric code AG(F,35P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66 (see above)
      3. linear OA(25², 5, F₂₅, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,25)), using
        discarding factors / shortening the dual code based on linear OA(25², 25, F₂₅, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
        Reedâ€“Solomon code RS(23,25) [i]
  2. linear OA(5¹, 3, F₅, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(5¹, s, F₅, 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.