MinT - Information on Result #2227104

Information on Result #2227104

Linear OA(3¹³, 18, F₃, 9) (dual of [18, 5, 10]-code), using 2 times truncation based on linear OA(3¹⁵, 20, F₃, 11) (dual of [20, 5, 12]-code), using

residual code [i] based on linear OA(3⁵⁰, 56, F₃, 35) (dual of [56, 6, 36]-code), using
- dual code (with bound on d by constructionÂ Y1) [i] based on
  1. linear OA(3⁶, 56, F₃, 3) (dual of [56, 50, 4]-code or 56-cap in PG(5,3)), using
    - the Hill cap [i]
  2. nonexistence of linear OA(3⁵, 21, F₃, 3) (dual of [21, 16, 4]-code or 21-cap in PG(4,3)), because
    - 20 is the largest size of a cap in PG(4,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(3¹³⁴, 139, F₃, 90) (dual of [139, 5, 91]-code)	[i]		Juxtaposition
2	Linear OA(3¹⁰⁵, 126, F₃, 50) (dual of [126, 21, 51]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound
3	Linear OA(3¹¹⁸, 142, F₃, 56) (dual of [142, 24, 57]-code)	[i]
4	Linear OA(3¹¹⁹, 144, F₃, 56) (dual of [144, 25, 57]-code)	[i]
5	Linear OA(3²⁰³, 239, F₃, 96) (dual of [239, 36, 97]-code)	[i]
6	Linear OA(3²⁰⁴, 241, F₃, 96) (dual of [241, 37, 97]-code)	[i]
7	Linear OA(3²⁰⁴, 240, F₃, 97) (dual of [240, 36, 98]-code)	[i]
8	Linear OA(3¹²⁷, 151, F₃, 61) (dual of [151, 24, 62]-code)	[i]
9	Linear OOA(3¹³, 9, F₃, 2, 9) (dual of [(9, 2), 5, 10]-NRT-code)	[i]		OOA Folding
10	Linear OOA(3¹³, 6, F₃, 3, 9) (dual of [(6, 3), 5, 10]-NRT-code)	[i]		OOA Folding