MinT - Information on Result #659063

Information on Result #659063

Linear OA(3¹⁵, 20, F₃, 11) (dual of [20, 5, 12]-code), using residual code 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(3¹⁴, 19, F₃, 10) (dual of [19, 5, 11]-code)	[i]		Truncation
2	Linear OA(3¹³, 18, F₃, 9) (dual of [18, 5, 10]-code)	[i]		Truncation
3	Linear OA(3¹³⁶, 141, F₃, 92) (dual of [141, 5, 93]-code)	[i]		Juxtaposition
4	Linear OA(3²⁴⁷, 263, F₃, 146) (dual of [263, 16, 147]-code)	[i]		ConstructionÂ X with Extended Narrow-Sense BCH Codes
5	Linear OA(3⁸¹, 102, F₃, 38) (dual of [102, 21, 39]-code)	[i]		ConstructionÂ XX with a Chain of Extended Narrow-Sense BCH Codes
6	Linear OA(3²⁰⁹, 246, F₃, 99) (dual of [246, 37, 100]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound
7	Linear OA(3²⁰⁹, 245, F₃, 100) (dual of [245, 36, 101]-code)	[i]
8	Linear OA(3²¹⁰, 247, F₃, 100) (dual of [247, 37, 101]-code)	[i]
9	Linear OA(3²¹⁰, 246, F₃, 101) (dual of [246, 36, 102]-code)	[i]
10	Linear OA(3²¹², 249, F₃, 101) (dual of [249, 37, 102]-code)	[i]
11	Linear OA(3²¹², 248, F₃, 102) (dual of [248, 36, 103]-code)	[i]
12	Linear OA(3²¹⁴, 251, F₃, 102) (dual of [251, 37, 103]-code)	[i]
13	Linear OA(3²¹⁴, 250, F₃, 103) (dual of [250, 36, 104]-code)	[i]
14	Linear OA(3²¹⁶, 253, F₃, 103) (dual of [253, 37, 104]-code)	[i]
15	Linear OA(3²¹⁶, 252, F₃, 104) (dual of [252, 36, 105]-code)	[i]
16	Linear OA(3²¹⁷, 254, F₃, 104) (dual of [254, 37, 105]-code)	[i]
17	Linear OOA(3¹⁵, 10, F₃, 2, 11) (dual of [(10, 2), 5, 12]-NRT-code)	[i]		OOA Folding