MinT - Information on Result #632783

Information on Result #632783

Linear OA(3¹⁷⁴, 189, F₃, 101) (dual of [189, 15, 102]-code), using concatenation of two codes based on

linear OA(27¹⁶, 21, F₂₇, 16) (dual of [21, 5, 17]-code or 21-arc in PG(15,27)), using
- discarding factors / shortening the dual code based on linear OA(27¹⁶, 27, F₂₇, 16) (dual of [27, 11, 17]-code or 27-arc in PG(15,27)), using
  - Reedâ€“Solomon code RS(11,27) [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(3¹⁷⁴, 189, F₃, 100) (dual of [189, 15, 101]-code)	[i]	Strength Reduction
2	Linear OA(3¹⁷⁴, 189, F₃, 99) (dual of [189, 15, 100]-code)	[i]
3	Linear OA(3¹⁷⁴, 189, F₃, 98) (dual of [189, 15, 99]-code)	[i]
4	Linear OA(3¹⁷⁴, 189, F₃, 97) (dual of [189, 15, 98]-code)	[i]
5	Linear OA(3¹⁷⁵, 190, F₃, 101) (dual of [190, 15, 102]-code)	[i]	Code Embedding in Larger Space
6	Linear OA(3¹⁷⁶, 191, F₃, 101) (dual of [191, 15, 102]-code)	[i]	Code Embedding in Larger Space
7	Linear OA(3¹⁷³, 188, F₃, 100) (dual of [188, 15, 101]-code)	[i]	Truncation
8	Linear OA(3¹⁷², 187, F₃, 99) (dual of [187, 15, 100]-code)	[i]
9	Linear OA(3¹⁷¹, 186, F₃, 98) (dual of [186, 15, 99]-code)	[i]
10	Linear OA(3¹⁷⁰, 185, F₃, 97) (dual of [185, 15, 98]-code)	[i]
11	Linear OA(3¹⁶⁹, 184, F₃, 96) (dual of [184, 15, 97]-code)	[i]
12	Linear OA(3¹⁶⁸, 183, F₃, 95) (dual of [183, 15, 96]-code)	[i]
13	Linear OA(3¹⁶⁶, 181, F₃, 93) (dual of [181, 15, 94]-code)	[i]
14	Linear OOA(3¹⁷⁴, 94, F₃, 2, 101) (dual of [(94, 2), 14, 102]-NRT-code)	[i]	OOA Folding
15	Linear OOA(3¹⁷⁴, 63, F₃, 3, 101) (dual of [(63, 3), 15, 102]-NRT-code)	[i]	OOA Folding