Information on Result #613002
Linear OA(4162, 16384, F4, 31) (dual of [16384, 16222, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31
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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(4177, 16400, F4, 31) (dual of [16400, 16223, 32]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(4180, 16405, F4, 31) (dual of [16405, 16225, 32]-code) | [i] | ||
| 3 | Linear OA(4181, 16407, F4, 31) (dual of [16407, 16226, 32]-code) | [i] | ||
| 4 | Linear OA(4183, 16411, F4, 31) (dual of [16411, 16228, 32]-code) | [i] | ||
| 5 | Linear OOA(4162, 8537, F4, 2, 31) (dual of [(8537, 2), 16912, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(4162, 8537, F4, 3, 31) (dual of [(8537, 3), 25449, 32]-NRT-code) | [i] | ||
| 7 | Digital (131, 162, 8537)-net over F4 | [i] | ||
| 8 | Linear OA(4183, 16406, F4, 31) (dual of [16406, 16223, 32]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 9 | Linear OA(4170, 16392, F4, 33) (dual of [16392, 16222, 34]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 10 | Linear OA(4162, 16391, F4, 31) (dual of [16391, 16229, 32]-code) | [i] | ✔ | |
| 11 | Linear OA(4179, 16401, F4, 34) (dual of [16401, 16222, 35]-code) | [i] | ✔ | |
| 12 | Linear OA(4163, 16399, F4, 31) (dual of [16399, 16236, 32]-code) | [i] | ✔ | |
| 13 | Linear OA(4188, 16410, F4, 35) (dual of [16410, 16222, 36]-code) | [i] | ✔ | |
| 14 | Linear OA(4167, 16410, F4, 31) (dual of [16410, 16243, 32]-code) | [i] | ✔ | |
| 15 | Linear OA(4200, 16422, F4, 37) (dual of [16422, 16222, 38]-code) | [i] | ✔ | |
| 16 | Linear OA(4197, 16419, F4, 36) (dual of [16419, 16222, 37]-code) | [i] | ✔ | |
| 17 | Linear OA(4169, 16419, F4, 31) (dual of [16419, 16250, 32]-code) | [i] | ✔ | |
| 18 | Linear OA(4210, 16432, F4, 38) (dual of [16432, 16222, 39]-code) | [i] | ✔ | |
| 19 | Linear OA(4172, 16429, F4, 31) (dual of [16429, 16257, 32]-code) | [i] | ✔ | |
| 20 | Linear OA(4220, 16442, F4, 39) (dual of [16442, 16222, 40]-code) | [i] | ✔ | |
| 21 | Linear OA(4178, 16442, F4, 31) (dual of [16442, 16264, 32]-code) | [i] | ✔ | |
| 22 | Linear OA(4230, 16449, F4, 41) (dual of [16449, 16219, 42]-code) | [i] | ✔ | |
| 23 | Linear OA(4233, 16455, F4, 41) (dual of [16455, 16222, 42]-code) | [i] | ✔ | |
| 24 | Linear OA(4180, 16448, F4, 31) (dual of [16448, 16268, 32]-code) | [i] | ✔ | |
| 25 | Linear OA(4183, 16454, F4, 31) (dual of [16454, 16271, 32]-code) | [i] | ✔ | |
| 26 | Linear OA(4244, 16466, F4, 42) (dual of [16466, 16222, 43]-code) | [i] | ✔ | |
| 27 | Linear OA(4184, 16462, F4, 31) (dual of [16462, 16278, 32]-code) | [i] | ✔ | |
| 28 | Linear OA(4255, 16474, F4, 43) (dual of [16474, 16219, 44]-code) | [i] | ✔ | |
| 29 | Linear OA(4256, 16477, F4, 43) (dual of [16477, 16221, 44]-code) | [i] | ✔ | |
| 30 | Linear OA(4199, 16420, F4, 37) (dual of [16420, 16221, 38]-code) | [i] | ✔ | |
| 31 | Linear OA(4231, 16452, F4, 41) (dual of [16452, 16221, 42]-code) | [i] | ✔ | |
| 32 | Linear OA(4232, 16454, F4, 41) (dual of [16454, 16222, 42]-code) | [i] | ✔ | |
| 33 | Linear OA(4230, 16452, F4, 40) (dual of [16452, 16222, 41]-code) | [i] | ✔ | |
| 34 | Linear OA(4181, 16452, F4, 31) (dual of [16452, 16271, 32]-code) | [i] | ✔ | |
| 35 | Linear OA(4242, 16458, F4, 42) (dual of [16458, 16216, 43]-code) | [i] | ✔ | |
| 36 | Linear OA(4183, 16456, F4, 31) (dual of [16456, 16273, 32]-code) | [i] | ✔ | |
| 37 | Linear OA(4255, 16477, F4, 43) (dual of [16477, 16222, 44]-code) | [i] | ✔ | |
| 38 | Linear OA(4254, 16474, F4, 43) (dual of [16474, 16220, 44]-code) | [i] | ✔ | |
| 39 | Linear OA(4199, 16421, F4, 37) (dual of [16421, 16222, 38]-code) | [i] | ✔ | |
| 40 | Linear OA(4208, 16426, F4, 38) (dual of [16426, 16218, 39]-code) | [i] | ✔ | |
| 41 | Linear OA(4209, 16430, F4, 38) (dual of [16430, 16221, 39]-code) | [i] | ✔ | |
| 42 | Linear OA(4171, 16428, F4, 31) (dual of [16428, 16257, 32]-code) | [i] | ✔ | |
| 43 | Linear OA(4218, 16440, F4, 39) (dual of [16440, 16222, 40]-code) | [i] | ✔ | |
| 44 | Linear OA(4176, 16440, F4, 31) (dual of [16440, 16264, 32]-code) | [i] | ✔ | |
| 45 | Linear OA(4230, 16450, F4, 41) (dual of [16450, 16220, 42]-code) | [i] | ✔ | |
| 46 | Linear OA(4179, 16447, F4, 31) (dual of [16447, 16268, 32]-code) | [i] | ✔ | |
| 47 | Linear OA(4199, 16417, F4, 37) (dual of [16417, 16218, 38]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 48 | Linear OA(4198, 16415, F4, 37) (dual of [16415, 16217, 38]-code) | [i] | ✔ | |
| 49 | Linear OA(4197, 16413, F4, 37) (dual of [16413, 16216, 38]-code) | [i] | ✔ | |
| 50 | Linear OA(4187, 16404, F4, 35) (dual of [16404, 16217, 36]-code) | [i] | ✔ | |
| 51 | Linear OA(4189, 16412, F4, 35) (dual of [16412, 16223, 36]-code) | [i] | ✔ | |
| 52 | Linear OA(4178, 16394, F4, 34) (dual of [16394, 16216, 35]-code) | [i] | ✔ | |
| 53 | Linear OA(4180, 16403, F4, 34) (dual of [16403, 16223, 35]-code) | [i] | ✔ | |
| 54 | Linear OA(4171, 16394, F4, 33) (dual of [16394, 16223, 34]-code) | [i] | ✔ | |
| 55 | Linear OA(4166, 16404, F4, 31) (dual of [16404, 16238, 32]-code) | [i] | ✔ | |
| 56 | Linear OA(4165, 16402, F4, 31) (dual of [16402, 16237, 32]-code) | [i] | ✔ | |
| 57 | Linear OA(4168, 16412, F4, 31) (dual of [16412, 16244, 32]-code) | [i] | ✔ | |
| 58 | Linear OOA(4162, 1092, F4, 31, 31) (dual of [(1092, 31), 33690, 32]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |