Information on Result #613128

Linear OA(4204, 16384, F4, 39) (dual of [16384, 16180, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39

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(4223, 16404, F4, 39) (dual of [16404, 16181, 40]-code) [i](u, u+v)-Construction
2Linear OA(4227, 16409, F4, 39) (dual of [16409, 16182, 40]-code) [i]
3Linear OA(4228, 16411, F4, 39) (dual of [16411, 16183, 40]-code) [i]
4Linear OA(4230, 16414, F4, 39) (dual of [16414, 16184, 40]-code) [i]
5Linear OOA(4204, 9788, F4, 2, 39) (dual of [(9788, 2), 19372, 40]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
6Linear OOA(4204, 9788, F4, 3, 39) (dual of [(9788, 3), 29160, 40]-NRT-code) [i]
7Digital (165, 204, 9788)-net over F4 [i]
8Linear OA(4231, 16412, F4, 39) (dual of [16412, 16181, 40]-code) [i](u, u−v, u+v+w)-Construction
9Linear OA(4212, 16392, F4, 41) (dual of [16392, 16180, 42]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
10Linear OA(4204, 16391, F4, 39) (dual of [16391, 16187, 40]-code) [i]✔
11Linear OA(4221, 16401, F4, 42) (dual of [16401, 16180, 43]-code) [i]✔
12Linear OA(4205, 16399, F4, 39) (dual of [16399, 16194, 40]-code) [i]✔
13Linear OA(4230, 16410, F4, 43) (dual of [16410, 16180, 44]-code) [i]✔
14Linear OA(4209, 16410, F4, 39) (dual of [16410, 16201, 40]-code) [i]✔
15Linear OA(4242, 16422, F4, 45) (dual of [16422, 16180, 46]-code) [i]✔
16Linear OA(4239, 16419, F4, 44) (dual of [16419, 16180, 45]-code) [i]✔
17Linear OA(4211, 16419, F4, 39) (dual of [16419, 16208, 40]-code) [i]✔
18Linear OA(4252, 16432, F4, 46) (dual of [16432, 16180, 47]-code) [i]✔
19Linear OA(4214, 16429, F4, 39) (dual of [16429, 16215, 40]-code) [i]✔
20Linear OA(4220, 16442, F4, 39) (dual of [16442, 16222, 40]-code) [i]✔
21Linear OA(4222, 16448, F4, 39) (dual of [16448, 16226, 40]-code) [i]✔
22Linear OA(4225, 16454, F4, 39) (dual of [16454, 16229, 40]-code) [i]✔
23Linear OA(4226, 16462, F4, 39) (dual of [16462, 16236, 40]-code) [i]✔
24Linear OA(4241, 16420, F4, 45) (dual of [16420, 16179, 46]-code) [i]✔
25Linear OA(4223, 16452, F4, 39) (dual of [16452, 16229, 40]-code) [i]✔
26Linear OA(4225, 16456, F4, 39) (dual of [16456, 16231, 40]-code) [i]✔
27Linear OA(4241, 16421, F4, 45) (dual of [16421, 16180, 46]-code) [i]✔
28Linear OA(4250, 16426, F4, 46) (dual of [16426, 16176, 47]-code) [i]✔
29Linear OA(4251, 16430, F4, 46) (dual of [16430, 16179, 47]-code) [i]✔
30Linear OA(4213, 16428, F4, 39) (dual of [16428, 16215, 40]-code) [i]✔
31Linear OA(4260, 16440, F4, 47) (dual of [16440, 16180, 48]-code) [i]✔
32Linear OA(4218, 16440, F4, 39) (dual of [16440, 16222, 40]-code) [i]✔
33Linear OA(4221, 16447, F4, 39) (dual of [16447, 16226, 40]-code) [i]✔
34Linear OA(4241, 16417, F4, 45) (dual of [16417, 16176, 46]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
35Linear OA(4240, 16415, F4, 45) (dual of [16415, 16175, 46]-code) [i]✔
36Linear OA(4239, 16413, F4, 45) (dual of [16413, 16174, 46]-code) [i]✔
37Linear OA(4229, 16404, F4, 43) (dual of [16404, 16175, 44]-code) [i]✔
38Linear OA(4231, 16412, F4, 43) (dual of [16412, 16181, 44]-code) [i]✔
39Linear OA(4220, 16394, F4, 42) (dual of [16394, 16174, 43]-code) [i]✔
40Linear OA(4222, 16403, F4, 42) (dual of [16403, 16181, 43]-code) [i]✔
41Linear OA(4213, 16394, F4, 41) (dual of [16394, 16181, 42]-code) [i]✔
42Linear OA(4208, 16404, F4, 39) (dual of [16404, 16196, 40]-code) [i]✔
43Linear OA(4207, 16402, F4, 39) (dual of [16402, 16195, 40]-code) [i]✔
44Linear OA(4210, 16412, F4, 39) (dual of [16412, 16202, 40]-code) [i]✔