Information on Result #738547
Linear OA(4227, 4178, F4, 45) (dual of [4178, 3951, 46]-code), using construction X applied to Ce(44) ⊂ Ce(32) based on
- linear OA(4199, 4096, F4, 45) (dual of [4096, 3897, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(4145, 4096, F4, 33) (dual of [4096, 3951, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(428, 82, F4, 11) (dual of [82, 54, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(428, 84, F4, 11) (dual of [84, 56, 12]-code), using
- (u, u−v, u+v+w)-construction [i] 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]
- linear OA(45, 27, F4, 3) (dual of [27, 22, 4]-code or 27-cap in PG(4,4)), using
- (u, u−v, u+v+w)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(428, 84, F4, 11) (dual of [84, 56, 12]-code), 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(4227, 4178, F4, 44) (dual of [4178, 3951, 45]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4229, 4180, F4, 45) (dual of [4180, 3951, 46]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(4230, 4181, F4, 45) (dual of [4181, 3951, 46]-code) | [i] | ||
| 4 | Linear OA(4226, 4177, F4, 44) (dual of [4177, 3951, 45]-code) | [i] | Truncation | |
| 5 | Linear OOA(4227, 2089, F4, 2, 45) (dual of [(2089, 2), 3951, 46]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(4227, 1392, F4, 3, 45) (dual of [(1392, 3), 3949, 46]-NRT-code) | [i] | ||