MinT - Information on Result #661540

Information on Result #661540

Linear OA(5¹⁴⁴, 210, F₅, 63) (dual of [210, 66, 64]-code), using concatenation of two codes based on

linear OA(25³⁷, 70, F₂₅, 31) (dual of [70, 33, 32]-code), using
- constructionÂ X applied to AG(F,33P) âŠ‚ AG(F,36P) [i] based on
  1. 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, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OA(25³², 65, F₂₅, 28) (dual of [65, 33, 29]-code), using algebraic-geometric code AG(F,36P) [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]
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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(5¹⁴³, 209, F₅, 62) (dual of [209, 66, 63]-code)	[i]		Truncation
2	Linear OOA(5¹⁴⁴, 105, F₅, 2, 63) (dual of [(105, 2), 66, 64]-NRT-code)	[i]		OOA Folding