Information on Result #679939
Linear OA(4181, 4121, F4, 39) (dual of [4121, 3940, 40]-code), using construction XX applied to Ce(38) ⊂ Ce(34) ⊂ Ce(33) based on
- linear OA(4175, 4096, F4, 39) (dual of [4096, 3921, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(4157, 4096, F4, 35) (dual of [4096, 3939, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(4151, 4096, F4, 34) (dual of [4096, 3945, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(45, 24, F4, 3) (dual of [24, 19, 4]-code or 24-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(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(4181, 4118, F4, 2, 39) (dual of [(4118, 2), 8055, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4181, 4118, F4, 3, 39) (dual of [(4118, 3), 12173, 40]-NRT-code) | [i] | ||
| 3 | Digital (142, 181, 4118)-net over F4 | [i] | ||
| 4 | Linear OOA(4181, 2060, F4, 2, 39) (dual of [(2060, 2), 3939, 40]-NRT-code) | [i] | OOA Folding | |