Information on Result #738437
Linear OA(428, 84, F4, 11) (dual of [84, 56, 12]-code), using (u, u−v, u+v+w)-construction based on
- linear OA(45, 27, F4, 3) (dual of [27, 22, 4]-code or 27-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- linear OA(48, 27, F4, 5) (dual of [27, 19, 6]-code), using
- linear OA(415, 30, F4, 11) (dual of [30, 15, 12]-code), using
- extended quadratic residue code Qe(30,4) [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 OOA(428, 83, F4, 2, 11) (dual of [(83, 2), 138, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(428, 83, F4, 3, 11) (dual of [(83, 3), 221, 12]-NRT-code) | [i] | ||
| 3 | Digital (17, 28, 83)-net over F4 | [i] | ||
| 4 | Linear OA(429, 91, F4, 11) (dual of [91, 62, 12]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OA(4239, 16469, F4, 41) (dual of [16469, 16230, 42]-code) | [i] | Construction X with Cyclic Codes | |
| 6 | Linear OA(4257, 4178, F4, 51) (dual of [4178, 3921, 52]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 7 | Linear OA(4251, 4178, F4, 50) (dual of [4178, 3927, 51]-code) | [i] | ||
| 8 | Linear OA(4245, 4178, F4, 49) (dual of [4178, 3933, 50]-code) | [i] | ||
| 9 | Linear OA(4239, 4178, F4, 47) (dual of [4178, 3939, 48]-code) | [i] | ||
| 10 | Linear OA(4233, 4178, F4, 46) (dual of [4178, 3945, 47]-code) | [i] | ||
| 11 | Linear OA(4227, 4178, F4, 45) (dual of [4178, 3951, 46]-code) | [i] | ||
| 12 | Linear OA(4221, 4178, F4, 43) (dual of [4178, 3957, 44]-code) | [i] | ||
| 13 | Linear OA(4215, 4178, F4, 42) (dual of [4178, 3963, 43]-code) | [i] | ||
| 14 | Linear OA(4209, 4178, F4, 41) (dual of [4178, 3969, 42]-code) | [i] | ||
| 15 | Linear OOA(428, 42, F4, 2, 11) (dual of [(42, 2), 56, 12]-NRT-code) | [i] | OOA Folding | |