Information on Result #2495503
Linear OOA(4154, 2097179, F4, 2, 18) (dual of [(2097179, 2), 4194204, 19]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4152, 2097178, F4, 2, 18) (dual of [(2097178, 2), 4194204, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4152, 4194356, F4, 18) (dual of [4194356, 4194204, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- linear OA(4144, 4194304, F4, 18) (dual of [4194304, 4194160, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(48, 52, F4, 4) (dual of [52, 44, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(48, 85, F4, 4) (dual of [85, 77, 5]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
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(4155, 2097179, F4, 2, 18) (dual of [(2097179, 2), 4194203, 19]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(4154, 2097179, F4, 3, 18) (dual of [(2097179, 3), 6291383, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (136, 154, 2097179)-net over F4 | [i] | ||