Information on Result #2494915
Linear OOA(4113, 2097158, F4, 2, 14) (dual of [(2097158, 2), 4194203, 15]-NRT-code), using 41 times duplication based on linear OOA(4112, 2097158, F4, 2, 14) (dual of [(2097158, 2), 4194204, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4112, 4194316, F4, 14) (dual of [4194316, 4194204, 15]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4111, 4194315, F4, 14) (dual of [4194315, 4194204, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(4111, 4194304, F4, 14) (dual of [4194304, 4194193, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(4100, 4194304, F4, 13) (dual of [4194304, 4194204, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(40, 11, F4, 0) (dual of [11, 11, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4111, 4194315, F4, 14) (dual of [4194315, 4194204, 15]-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 OOA(4113, 1946362, F4, 3, 14) (dual of [(1946362, 3), 5838973, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (99, 113, 1946362)-net over F4 | [i] | ||