MinT - Information on Result #2247239

Information on Result #2247239

Linear OA(5¹⁴⁵, 209, F₅, 64) (dual of [209, 64, 65]-code), using 1 times truncation 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

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(5¹⁴⁷, 211, F₅, 64) (dual of [211, 64, 65]-code)	[i]		Code Embedding in Larger Space
2	Linear OOA(5¹⁴⁵, 104, F₅, 2, 64) (dual of [(104, 2), 63, 65]-NRT-code)	[i]		OOA Folding