MinT - Information on Result #2247238

Information on Result #2247238

Linear OA(5¹⁴⁷, 209, F₅, 66) (dual of [209, 62, 67]-code), using 1 times truncation based on linear OA(5¹⁴⁸, 210, F₅, 67) (dual of [210, 62, 68]-code), using

concatenation of two codes [i] based on
1. linear OA(25³⁹, 70, F₂₅, 33) (dual of [70, 31, 34]-code), using
  - constructionÂ X applied to AG(F,31P) âŠ‚ AG(F,34P) [i] based on
    1. linear OA(25³⁷, 65, F₂₅, 33) (dual of [65, 28, 34]-code), using algebraic-geometric code AG(F,31P) [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(25³⁴, 65, F₂₅, 30) (dual of [65, 31, 31]-code), using algebraic-geometric code AG(F,34P) [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		Method
1	Linear OA(5¹⁴⁹, 211, F₅, 66) (dual of [211, 62, 67]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(5¹⁵⁰, 212, F₅, 66) (dual of [212, 62, 67]-code)	[i]	Code Embedding in Larger Space
3	Linear OOA(5¹⁴⁷, 104, F₅, 2, 66) (dual of [(104, 2), 61, 67]-NRT-code)	[i]	OOA Folding