Information on Result #613105

Linear OA(4190, 16384, F4, 37) (dual of [16384, 16194, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37

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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(4189, 16383, F4, 36) (dual of [16383, 16194, 37]-code) [i]Truncation
2Linear OA(4208, 16403, F4, 37) (dual of [16403, 16195, 38]-code) [i](u, u+v)-Construction
3Linear OA(4212, 16408, F4, 37) (dual of [16408, 16196, 38]-code) [i]
4Linear OA(4213, 16410, F4, 37) (dual of [16410, 16197, 38]-code) [i]
5Linear OA(4215, 16413, F4, 37) (dual of [16413, 16198, 38]-code) [i]
6Linear OOA(4190, 8238, F4, 2, 37) (dual of [(8238, 2), 16286, 38]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
7Linear OOA(4190, 8238, F4, 3, 37) (dual of [(8238, 3), 24524, 38]-NRT-code) [i]
8Digital (153, 190, 8238)-net over F4 [i]
9Linear OA(4215, 16410, F4, 37) (dual of [16410, 16195, 38]-code) [i](u, u−v, u+v+w)-Construction
10Linear OA(4197, 16391, F4, 38) (dual of [16391, 16194, 39]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
11Linear OA(4191, 16392, F4, 37) (dual of [16392, 16201, 38]-code) [i]✔
12Linear OA(4205, 16399, F4, 39) (dual of [16399, 16194, 40]-code) [i]✔
13Linear OA(4191, 16399, F4, 36) (dual of [16399, 16208, 37]-code) [i]✔
14Linear OA(4193, 16401, F4, 37) (dual of [16401, 16208, 38]-code) [i]✔
15Linear OA(4216, 16410, F4, 41) (dual of [16410, 16194, 42]-code) [i]✔
16Linear OA(4214, 16405, F4, 40) (dual of [16405, 16191, 41]-code) [i]✔
17Linear OA(4195, 16410, F4, 37) (dual of [16410, 16215, 38]-code) [i]✔
18Linear OA(4193, 16405, F4, 36) (dual of [16405, 16212, 37]-code) [i]✔
19Linear OA(4225, 16419, F4, 42) (dual of [16419, 16194, 43]-code) [i]✔
20Linear OA(4200, 16422, F4, 37) (dual of [16422, 16222, 38]-code) [i]✔
21Linear OA(4197, 16419, F4, 36) (dual of [16419, 16222, 37]-code) [i]✔
22Linear OA(4235, 16429, F4, 43) (dual of [16429, 16194, 44]-code) [i]✔
23Linear OA(4203, 16432, F4, 37) (dual of [16432, 16229, 38]-code) [i]✔
24Linear OA(4200, 16429, F4, 36) (dual of [16429, 16229, 37]-code) [i]✔
25Linear OA(4248, 16442, F4, 45) (dual of [16442, 16194, 46]-code) [i]✔
26Linear OA(4245, 16439, F4, 44) (dual of [16439, 16194, 45]-code) [i]✔
27Linear OA(4206, 16442, F4, 37) (dual of [16442, 16236, 38]-code) [i]✔
28Linear OA(4203, 16439, F4, 36) (dual of [16439, 16236, 37]-code) [i]✔
29Linear OA(4257, 16448, F4, 46) (dual of [16448, 16191, 47]-code) [i]✔
30Linear OA(4260, 16454, F4, 46) (dual of [16454, 16194, 47]-code) [i]✔
31Linear OA(4209, 16449, F4, 37) (dual of [16449, 16240, 38]-code) [i]✔
32Linear OA(4212, 16455, F4, 37) (dual of [16455, 16243, 38]-code) [i]✔
33Linear OA(4216, 16466, F4, 37) (dual of [16466, 16250, 38]-code) [i]✔
34Linear OA(4212, 16462, F4, 36) (dual of [16462, 16250, 37]-code) [i]✔
35Linear OA(4199, 16420, F4, 37) (dual of [16420, 16221, 38]-code) [i]✔
36Linear OA(4258, 16452, F4, 46) (dual of [16452, 16194, 47]-code) [i]✔
37Linear OA(4210, 16452, F4, 37) (dual of [16452, 16242, 38]-code) [i]✔
38Linear OA(4211, 16454, F4, 37) (dual of [16454, 16243, 38]-code) [i]✔
39Linear OA(4209, 16452, F4, 36) (dual of [16452, 16243, 37]-code) [i]✔
40Linear OA(4214, 16458, F4, 37) (dual of [16458, 16244, 38]-code) [i]✔
41Linear OA(4211, 16456, F4, 36) (dual of [16456, 16245, 37]-code) [i]✔
42Linear OA(4199, 16421, F4, 37) (dual of [16421, 16222, 38]-code) [i]✔
43Linear OA(4234, 16428, F4, 43) (dual of [16428, 16194, 44]-code) [i]✔
44Linear OA(4201, 16426, F4, 37) (dual of [16426, 16225, 38]-code) [i]✔
45Linear OA(4202, 16430, F4, 37) (dual of [16430, 16228, 38]-code) [i]✔
46Linear OA(4199, 16428, F4, 36) (dual of [16428, 16229, 37]-code) [i]✔
47Linear OA(4246, 16440, F4, 45) (dual of [16440, 16194, 46]-code) [i]✔
48Linear OA(4204, 16440, F4, 37) (dual of [16440, 16236, 38]-code) [i]✔
49Linear OA(4256, 16447, F4, 46) (dual of [16447, 16191, 47]-code) [i]✔
50Linear OA(4257, 16451, F4, 46) (dual of [16451, 16194, 47]-code) [i]✔
51Linear OA(4209, 16450, F4, 37) (dual of [16450, 16241, 38]-code) [i]✔
52Linear OA(4224, 16412, F4, 42) (dual of [16412, 16188, 43]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
53Linear OA(4215, 16403, F4, 41) (dual of [16403, 16188, 42]-code) [i]✔
54Linear OA(4213, 16401, F4, 40) (dual of [16401, 16188, 41]-code) [i]✔
55Linear OA(4220, 16417, F4, 41) (dual of [16417, 16197, 42]-code) [i]✔
56Linear OA(4219, 16415, F4, 41) (dual of [16415, 16196, 42]-code) [i]✔
57Linear OA(4218, 16413, F4, 41) (dual of [16413, 16195, 42]-code) [i]✔
58Linear OA(4208, 16404, F4, 39) (dual of [16404, 16196, 40]-code) [i]✔
59Linear OA(4207, 16402, F4, 39) (dual of [16402, 16195, 40]-code) [i]✔
60Linear OA(4199, 16394, F4, 38) (dual of [16394, 16195, 39]-code) [i]✔
61Linear OA(4192, 16394, F4, 37) (dual of [16394, 16202, 38]-code) [i]✔
62Linear OA(4194, 16403, F4, 37) (dual of [16403, 16209, 38]-code) [i]✔
63Linear OA(4192, 16401, F4, 36) (dual of [16401, 16209, 37]-code) [i]✔
64Linear OA(4199, 16417, F4, 37) (dual of [16417, 16218, 38]-code) [i]✔
65Linear OA(4198, 16415, F4, 37) (dual of [16415, 16217, 38]-code) [i]✔
66Linear OA(4197, 16413, F4, 37) (dual of [16413, 16216, 38]-code) [i]✔
67Linear OOA(4190, 8192, F4, 2, 37) (dual of [(8192, 2), 16194, 38]-NRT-code) [i]OOA Folding
68Linear OOA(4190, 5461, F4, 3, 37) (dual of [(5461, 3), 16193, 38]-NRT-code) [i]