MinT - Information on Result #2247237

Information on Result #2247237

Linear OA(5¹⁴⁹, 209, F₅, 68) (dual of [209, 60, 69]-code), using 1 times truncation based on linear OA(5¹⁵⁰, 210, F₅, 69) (dual of [210, 60, 70]-code), using

concatenation of two codes [i] based on
1. linear OA(25⁴⁰, 70, F₂₅, 34) (dual of [70, 30, 35]-code), using
  - constructionÂ X applied to AG(F,30P) âŠ‚ AG(F,33P) [i] based on
    1. linear OA(25³⁸, 65, F₂₅, 34) (dual of [65, 27, 35]-code), using algebraic-geometric code AG(F,30P) [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(25³⁵, 65, F₂₅, 31) (dual of [65, 30, 32]-code), using algebraic-geometric code AG(F,33P) [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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(5¹⁴⁹, 104, F₅, 2, 68) (dual of [(104, 2), 59, 69]-NRT-code)	[i]		OOA Folding