Information on Result #2495348
Linear OOA(4141, 2097172, F4, 2, 17) (dual of [(2097172, 2), 4194203, 18]-NRT-code), using 41 times duplication based on linear OOA(4140, 2097172, F4, 2, 17) (dual of [(2097172, 2), 4194204, 18]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4138, 2097171, F4, 2, 17) (dual of [(2097171, 2), 4194204, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4138, 4194342, F4, 17) (dual of [4194342, 4194204, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(4133, 4194304, F4, 17) (dual of [4194304, 4194171, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(45, 38, F4, 3) (dual of [38, 33, 4]-code or 38-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
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- OOA 2-folding [i] based on linear OA(4138, 4194342, F4, 17) (dual of [4194342, 4194204, 18]-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(4141, 1913946, F4, 3, 17) (dual of [(1913946, 3), 5741697, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (124, 141, 1913946)-net over F4 | [i] | ||