MinT - Information on Result #632780

Information on Result #632780

Linear OA(3²¹⁰, 243, F₃, 101) (dual of [243, 33, 102]-code), using concatenation of two codes 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.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(3²¹⁰, 243, F₃, 100) (dual of [243, 33, 101]-code)	[i]		Strength Reduction
2	Linear OA(3²¹⁰, 243, F₃, 99) (dual of [243, 33, 100]-code)	[i]
3	Linear OA(3²¹⁰, 243, F₃, 98) (dual of [243, 33, 99]-code)	[i]
4	Linear OA(3²¹¹, 244, F₃, 101) (dual of [244, 33, 102]-code)	[i]		Code Embedding in Larger Space
5	Linear OA(3²¹², 245, F₃, 101) (dual of [245, 33, 102]-code)	[i]		Code Embedding in Larger Space
6	Linear OA(3²⁰⁹, 242, F₃, 100) (dual of [242, 33, 101]-code)	[i]		Truncation
7	Linear OA(3²⁰⁸, 241, F₃, 99) (dual of [241, 33, 100]-code)	[i]
8	Linear OA(3²⁰⁷, 240, F₃, 98) (dual of [240, 33, 99]-code)	[i]
9	Linear OA(3²⁰⁶, 239, F₃, 97) (dual of [239, 33, 98]-code)	[i]
10	Linear OA(3²⁰⁵, 238, F₃, 96) (dual of [238, 33, 97]-code)	[i]
11	Linear OOA(3²¹⁰, 81, F₃, 3, 101) (dual of [(81, 3), 33, 102]-NRT-code)	[i]		OOA Folding