MinT - Information on Result #632768

Information on Result #632768

Linear OA(3¹⁵⁰, 162, F₃, 89) (dual of [162, 12, 90]-code), using concatenation of two codes based on

linear OA(27¹⁴, 18, F₂₇, 14) (dual of [18, 4, 15]-code or 18-arc in PG(13,27)), using
- discarding factors / shortening the dual code based on linear OA(27¹⁴, 27, F₂₇, 14) (dual of [27, 13, 15]-code or 27-arc in PG(13,27)), using
  - Reedâ€“Solomon code RS(13,27) [i]
linear OA(3⁶, 9, F₃, 5) (dual of [9, 3, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(3⁶, 10, F₃, 5) (dual of [10, 4, 6]-code), using
  - projective code from ovoid in PG(3,Â 3) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OA(3¹⁵⁰, 162, F₃, 88) (dual of [162, 12, 89]-code)	[i]	Strength Reduction
2	Linear OA(3¹⁵⁰, 162, F₃, 87) (dual of [162, 12, 88]-code)	[i]
3	Linear OA(3¹⁵⁰, 162, F₃, 86) (dual of [162, 12, 87]-code)	[i]
4	Linear OA(3¹⁵¹, 163, F₃, 89) (dual of [163, 12, 90]-code)	[i]	Code Embedding in Larger Space
5	Linear OA(3¹⁵², 164, F₃, 89) (dual of [164, 12, 90]-code)	[i]	Code Embedding in Larger Space
6	Linear OA(3¹⁴⁹, 161, F₃, 88) (dual of [161, 12, 89]-code)	[i]	Truncation
7	Linear OA(3¹⁴⁸, 160, F₃, 87) (dual of [160, 12, 88]-code)	[i]
8	Linear OA(3¹⁴⁷, 159, F₃, 86) (dual of [159, 12, 87]-code)	[i]
9	Linear OA(3¹⁴⁶, 158, F₃, 85) (dual of [158, 12, 86]-code)	[i]
10	Linear OA(3¹⁴⁵, 157, F₃, 84) (dual of [157, 12, 85]-code)	[i]
11	Linear OA(3¹⁴³, 155, F₃, 82) (dual of [155, 12, 83]-code)	[i]
12	Linear OOA(3¹⁵⁰, 81, F₃, 2, 89) (dual of [(81, 2), 12, 90]-NRT-code)	[i]	OOA Folding
13	Linear OOA(3¹⁵⁰, 54, F₃, 3, 89) (dual of [(54, 3), 12, 90]-NRT-code)	[i]	OOA Folding