MinT - Information on Result #638074

Information on Result #638074

Linear OA(5¹⁴⁸, 168, F₅, 89) (dual of [168, 20, 90]-code), using concatenation of two codes based on

linear OA(25³², 42, F₂₅, 29) (dual of [42, 10, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(25³², 52, F₂₅, 29) (dual of [52, 20, 30]-code), using
  - extended algebraic-geometric code AG_e(F,22P) [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
    - a function field by GarcÃa and Quoos [i]
linear OA(5², 4, F₅, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,5)), using
- discarding factors / shortening the dual code based on linear OA(5², 5, F₅, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,5)), using
  - Reedâ€“Solomon code RS(3,5) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OA(5¹⁴⁸, 168, F₅, 88) (dual of [168, 20, 89]-code)	[i]	Strength Reduction
2	Linear OA(5¹⁴⁹, 169, F₅, 89) (dual of [169, 20, 90]-code)	[i]	Code Embedding in Larger Space
3	Linear OA(5¹⁴⁷, 167, F₅, 88) (dual of [167, 20, 89]-code)	[i]	Truncation
4	Linear OA(5¹⁴⁶, 166, F₅, 87) (dual of [166, 20, 88]-code)	[i]
5	Linear OA(5¹⁴⁵, 165, F₅, 86) (dual of [165, 20, 87]-code)	[i]
6	Linear OOA(5¹⁴⁸, 84, F₅, 2, 89) (dual of [(84, 2), 20, 90]-NRT-code)	[i]	OOA Folding
7	Linear OOA(5¹⁴⁸, 56, F₅, 3, 89) (dual of [(56, 3), 20, 90]-NRT-code)	[i]	OOA Folding