MinT - Information on Result #661542

Information on Result #661542

Linear OA(5¹⁴⁶, 210, F₅, 65) (dual of [210, 64, 66]-code), using concatenation of two codes based on

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]
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		Method
1	Linear OA(5¹⁴⁶, 210, F₅, 64) (dual of [210, 64, 65]-code)	[i]	Strength Reduction
2	Linear OA(5¹⁴⁷, 211, F₅, 65) (dual of [211, 64, 66]-code)	[i]	Code Embedding in Larger Space
3	Linear OA(5¹⁴⁸, 212, F₅, 65) (dual of [212, 64, 66]-code)	[i]
4	Linear OA(5¹⁴⁹, 213, F₅, 65) (dual of [213, 64, 66]-code)	[i]
5	Linear OA(5¹⁴⁵, 209, F₅, 64) (dual of [209, 64, 65]-code)	[i]	Truncation
6	Linear OOA(5¹⁴⁶, 105, F₅, 2, 65) (dual of [(105, 2), 64, 66]-NRT-code)	[i]	OOA Folding
7	Linear OOA(5¹⁴⁶, 70, F₅, 3, 65) (dual of [(70, 3), 64, 66]-NRT-code)	[i]	OOA Folding