MinT - Information on Result #632766

Information on Result #632766

Linear OA(3¹⁶⁸, 189, F₃, 89) (dual of [189, 21, 90]-code), using concatenation of two codes based on

linear OA(27¹⁴, 21, F₂₇, 14) (dual of [21, 7, 15]-code or 21-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(3¹⁶⁸, 189, F₃, 88) (dual of [189, 21, 89]-code)	[i]	Strength Reduction
2	Linear OA(3¹⁶⁸, 189, F₃, 87) (dual of [189, 21, 88]-code)	[i]
3	Linear OA(3¹⁶⁸, 189, F₃, 86) (dual of [189, 21, 87]-code)	[i]
4	Linear OA(3¹⁶⁸, 189, F₃, 85) (dual of [189, 21, 86]-code)	[i]
5	Linear OA(3¹⁶⁹, 190, F₃, 89) (dual of [190, 21, 90]-code)	[i]	Code Embedding in Larger Space
6	Linear OA(3¹⁷⁰, 191, F₃, 89) (dual of [191, 21, 90]-code)	[i]	Code Embedding in Larger Space
7	Linear OA(3¹⁶⁷, 188, F₃, 88) (dual of [188, 21, 89]-code)	[i]	Truncation
8	Linear OA(3¹⁶⁶, 187, F₃, 87) (dual of [187, 21, 88]-code)	[i]
9	Linear OA(3¹⁶⁵, 186, F₃, 86) (dual of [186, 21, 87]-code)	[i]
10	Linear OA(3¹⁶⁴, 185, F₃, 85) (dual of [185, 21, 86]-code)	[i]
11	Linear OA(3¹⁶², 183, F₃, 83) (dual of [183, 21, 84]-code)	[i]
12	Linear OA(3¹⁶¹, 182, F₃, 82) (dual of [182, 21, 83]-code)	[i]
13	Linear OA(3¹⁶⁰, 181, F₃, 81) (dual of [181, 21, 82]-code)	[i]
14	Linear OA(3¹⁵⁸, 179, F₃, 79) (dual of [179, 21, 80]-code)	[i]
15	Linear OA(3¹⁵⁷, 178, F₃, 78) (dual of [178, 21, 79]-code)	[i]
16	Linear OOA(3¹⁶⁸, 63, F₃, 3, 89) (dual of [(63, 3), 21, 90]-NRT-code)	[i]	OOA Folding