Information on Result #679398
Linear OA(4194, 4110, F4, 43) (dual of [4110, 3916, 44]-code), using construction X applied to C([0,21]) ⊂ C([0,20]) based on
- linear OA(4193, 4097, F4, 43) (dual of [4097, 3904, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(4181, 4097, F4, 41) (dual of [4097, 3916, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(41, 13, F4, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
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(4195, 4111, F4, 43) (dual of [4111, 3916, 44]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4196, 4112, F4, 43) (dual of [4112, 3916, 44]-code) | [i] | ||
| 3 | Linear OOA(4194, 3639, F4, 2, 43) (dual of [(3639, 2), 7084, 44]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(4194, 3639, F4, 3, 43) (dual of [(3639, 3), 10723, 44]-NRT-code) | [i] | ||
| 5 | Digital (151, 194, 3639)-net over F4 | [i] | ||
| 6 | Linear OA(4196, 4114, F4, 43) (dual of [4114, 3918, 44]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OA(4197, 4121, F4, 43) (dual of [4121, 3924, 44]-code) | [i] | ||
| 8 | Linear OA(4198, 4135, F4, 43) (dual of [4135, 3937, 44]-code) | [i] | ||
| 9 | Linear OA(4199, 4160, F4, 43) (dual of [4160, 3961, 44]-code) | [i] | ||
| 10 | Linear OA(4200, 4205, F4, 43) (dual of [4205, 4005, 44]-code) | [i] | ||
| 11 | Linear OA(4201, 4277, F4, 43) (dual of [4277, 4076, 44]-code) | [i] | ||
| 12 | Linear OA(4202, 4379, F4, 43) (dual of [4379, 4177, 44]-code) | [i] | ||
| 13 | Linear OA(4203, 4506, F4, 43) (dual of [4506, 4303, 44]-code) | [i] | ||
| 14 | Linear OA(4196, 4113, F4, 43) (dual of [4113, 3917, 44]-code) | [i] | Construction X with Varšamov Bound | |
| 15 | Linear OA(4197, 4115, F4, 43) (dual of [4115, 3918, 44]-code) | [i] | ||
| 16 | Linear OOA(4194, 2055, F4, 2, 43) (dual of [(2055, 2), 3916, 44]-NRT-code) | [i] | OOA Folding | |
| 17 | Linear OOA(4194, 1370, F4, 3, 43) (dual of [(1370, 3), 3916, 44]-NRT-code) | [i] | ||