MinT - Information on Result #632805

Information on Result #632805

Linear OA(3²¹⁹, 234, F₃, 131) (dual of [234, 15, 132]-code), using concatenation of two codes based on

linear OA(27²¹, 26, F₂₇, 21) (dual of [26, 5, 22]-code or 26-arc in PG(20,27)), using
- discarding factors / shortening the dual code based on linear OA(27²¹, 27, F₂₇, 21) (dual of [27, 6, 22]-code or 27-arc in PG(20,27)), using
  - Reedâ€“Solomon code RS(6,27) [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(3²¹⁹, 234, F₃, 130) (dual of [234, 15, 131]-code)	[i]	Strength Reduction
2	Linear OA(3²¹⁹, 234, F₃, 129) (dual of [234, 15, 130]-code)	[i]	Strength Reduction
3	Linear OA(3²²⁰, 235, F₃, 131) (dual of [235, 15, 132]-code)	[i]	Code Embedding in Larger Space
4	Linear OA(3²²¹, 236, F₃, 131) (dual of [236, 15, 132]-code)	[i]	Code Embedding in Larger Space
5	Linear OA(3²¹⁸, 233, F₃, 130) (dual of [233, 15, 131]-code)	[i]	Truncation
6	Linear OA(3²¹⁷, 232, F₃, 129) (dual of [232, 15, 130]-code)	[i]
7	Linear OA(3²¹⁶, 231, F₃, 128) (dual of [231, 15, 129]-code)	[i]
8	Linear OA(3²¹⁵, 230, F₃, 127) (dual of [230, 15, 128]-code)	[i]
9	Linear OA(3²¹⁴, 229, F₃, 126) (dual of [229, 15, 127]-code)	[i]
10	Linear OA(3²¹³, 228, F₃, 125) (dual of [228, 15, 126]-code)	[i]
11	Linear OA(3²¹², 227, F₃, 124) (dual of [227, 15, 125]-code)	[i]
12	Linear OA(3²¹¹, 226, F₃, 123) (dual of [226, 15, 124]-code)	[i]
13	Linear OA(3²⁰⁹, 224, F₃, 121) (dual of [224, 15, 122]-code)	[i]
14	Linear OA(3²⁰⁸, 223, F₃, 120) (dual of [223, 15, 121]-code)	[i]
15	Linear OOA(3²¹⁹, 117, F₃, 2, 131) (dual of [(117, 2), 15, 132]-NRT-code)	[i]	OOA Folding
16	Linear OOA(3²¹⁹, 78, F₃, 3, 131) (dual of [(78, 3), 15, 132]-NRT-code)	[i]	OOA Folding