MinT - Information on Result #661834

Information on Result #661834

Linear OA(3¹⁶¹, 168, F₃, 107) (dual of [168, 7, 108]-code), using (u,Â uâˆ’v,Â u+v+w)-construction 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]
linear OA(3⁵⁵, 56, F₃, 53) (dual of [56, 1, 54]-code), using
- strength reduction [i] based on linear OA(3⁵⁵, 56, F₃, 55) (dual of [56, 1, 56]-code or 56-arc in PG(54,3)), using
  - dual of repetition code with length 56 [i]
linear OA(3⁵⁶, 56, F₃, 56) (dual of [56, 0, 57]-code or 56-arc in PG(55,3)), using
- complete OA / dual of code with only one code word [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		Method
1	Linear OA(3¹⁶¹, 168, F₃, 106) (dual of [168, 7, 107]-code)	[i]	Strength Reduction
2	Linear OA(3¹⁶¹, 168, F₃, 105) (dual of [168, 7, 106]-code)	[i]
3	Linear OA(3¹⁶¹, 168, F₃, 104) (dual of [168, 7, 105]-code)	[i]
4	Linear OA(3¹⁶¹, 168, F₃, 103) (dual of [168, 7, 104]-code)	[i]
5	Linear OA(3¹⁶¹, 168, F₃, 102) (dual of [168, 7, 103]-code)	[i]
6	Linear OA(3¹⁶², 169, F₃, 107) (dual of [169, 7, 108]-code)	[i]	Code Embedding in Larger Space
7	Linear OA(3¹⁶³, 170, F₃, 107) (dual of [170, 7, 108]-code)	[i]
8	Linear OA(3¹⁶⁴, 171, F₃, 107) (dual of [171, 7, 108]-code)	[i]
9	Linear OA(3¹⁶⁵, 172, F₃, 107) (dual of [172, 7, 108]-code)	[i]
10	Linear OA(3¹⁶⁶, 173, F₃, 107) (dual of [173, 7, 108]-code)	[i]
11	Linear OA(3¹⁶⁰, 167, F₃, 106) (dual of [167, 7, 107]-code)	[i]	Truncation
12	Linear OA(3¹⁵⁹, 166, F₃, 105) (dual of [166, 7, 106]-code)	[i]
13	Linear OA(3¹⁵⁸, 165, F₃, 104) (dual of [165, 7, 105]-code)	[i]
14	Linear OA(3¹⁵⁷, 164, F₃, 103) (dual of [164, 7, 104]-code)	[i]
15	Linear OA(3¹⁵⁶, 163, F₃, 102) (dual of [163, 7, 103]-code)	[i]
16	Linear OA(3¹⁵⁴, 161, F₃, 100) (dual of [161, 7, 101]-code)	[i]
17	Linear OA(3¹⁶⁸, 175, F₃, 108) (dual of [175, 7, 109]-code)	[i]	Juxtaposition
18	Linear OA(3¹⁶⁹, 176, F₃, 109) (dual of [176, 7, 110]-code)	[i]
19	Linear OA(3¹⁷¹, 178, F₃, 110) (dual of [178, 7, 111]-code)	[i]
20	Linear OA(3¹⁷³, 180, F₃, 111) (dual of [180, 7, 112]-code)	[i]
21	Linear OA(3¹⁷⁴, 181, F₃, 112) (dual of [181, 7, 113]-code)	[i]
22	Linear OA(3¹⁷⁵, 182, F₃, 113) (dual of [182, 7, 114]-code)	[i]
23	Linear OA(3¹⁷⁸, 185, F₃, 114) (dual of [185, 7, 115]-code)	[i]
24	Linear OA(3¹⁷⁹, 186, F₃, 115) (dual of [186, 7, 116]-code)	[i]
25	Linear OA(3¹⁸⁰, 187, F₃, 116) (dual of [187, 7, 117]-code)	[i]
26	Linear OA(3¹⁸³, 190, F₃, 117) (dual of [190, 7, 118]-code)	[i]
27	Linear OA(3¹⁸⁴, 191, F₃, 118) (dual of [191, 7, 119]-code)	[i]
28	Linear OA(3¹⁸⁵, 192, F₃, 119) (dual of [192, 7, 120]-code)	[i]
29	Linear OA(3¹⁸⁶, 193, F₃, 120) (dual of [193, 7, 121]-code)	[i]
30	Linear OA(3¹⁸⁷, 194, F₃, 121) (dual of [194, 7, 122]-code)	[i]
31	Linear OA(3¹⁸⁸, 195, F₃, 122) (dual of [195, 7, 123]-code)	[i]
32	Linear OA(3¹⁹⁴, 201, F₃, 123) (dual of [201, 7, 124]-code)	[i]
33	Linear OA(3¹⁹⁵, 202, F₃, 124) (dual of [202, 7, 125]-code)	[i]
34	Linear OA(3¹⁹⁶, 203, F₃, 125) (dual of [203, 7, 126]-code)	[i]
35	Linear OA(3¹⁹⁸, 205, F₃, 126) (dual of [205, 7, 127]-code)	[i]
36	Linear OA(3¹⁹⁹, 206, F₃, 127) (dual of [206, 7, 128]-code)	[i]
37	Linear OA(3²⁰⁰, 207, F₃, 128) (dual of [207, 7, 129]-code)	[i]
38	Linear OA(3²⁰¹, 208, F₃, 129) (dual of [208, 7, 130]-code)	[i]
39	Linear OA(3²⁰², 209, F₃, 130) (dual of [209, 7, 131]-code)	[i]
40	Linear OA(3²⁰³, 210, F₃, 131) (dual of [210, 7, 132]-code)	[i]
41	Linear OA(3²⁰⁷, 214, F₃, 132) (dual of [214, 7, 133]-code)	[i]
42	Linear OA(3²⁰⁸, 215, F₃, 133) (dual of [215, 7, 134]-code)	[i]
43	Linear OA(3²¹⁰, 217, F₃, 134) (dual of [217, 7, 135]-code)	[i]
44	Linear OA(3²¹², 219, F₃, 135) (dual of [219, 7, 136]-code)	[i]
45	Linear OA(3²¹³, 220, F₃, 136) (dual of [220, 7, 137]-code)	[i]
46	Linear OA(3²¹⁴, 221, F₃, 137) (dual of [221, 7, 138]-code)	[i]
47	Linear OA(3²³⁷, 244, F₃, 153) (dual of [244, 7, 154]-code)	[i]
48	Linear OA(3²³⁸, 245, F₃, 154) (dual of [245, 7, 155]-code)	[i]
49	Linear OA(3²³⁹, 246, F₃, 155) (dual of [246, 7, 156]-code)	[i]
50	Linear OA(3²⁴⁰, 247, F₃, 156) (dual of [247, 7, 157]-code)	[i]
51	Linear OA(3²⁴¹, 248, F₃, 157) (dual of [248, 7, 158]-code)	[i]
52	Linear OA(3²⁴², 249, F₃, 158) (dual of [249, 7, 159]-code)	[i]
53	Linear OA(3¹⁹¹, 198, F₃, 123) (dual of [198, 7, 124]-code)	[i]
54	Linear OA(3¹⁹², 199, F₃, 124) (dual of [199, 7, 125]-code)	[i]
55	Linear OA(3¹⁹⁴, 201, F₃, 125) (dual of [201, 7, 126]-code)	[i]
56	Linear OA(3¹⁸², 189, F₃, 117) (dual of [189, 7, 118]-code)	[i]
57	Linear OOA(3¹⁶¹, 84, F₃, 2, 107) (dual of [(84, 2), 7, 108]-NRT-code)	[i]	OOA Folding
58	Linear OOA(3¹⁶¹, 56, F₃, 3, 107) (dual of [(56, 3), 7, 108]-NRT-code)	[i]	OOA Folding