Information on Result #2496303
Linear OOA(4215, 2097187, F4, 2, 25) (dual of [(2097187, 2), 4194159, 26]-NRT-code), using 41 times duplication based on linear OOA(4214, 2097187, F4, 2, 25) (dual of [(2097187, 2), 4194160, 26]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4212, 2097186, F4, 2, 25) (dual of [(2097186, 2), 4194160, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4212, 4194372, F4, 25) (dual of [4194372, 4194160, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- linear OA(4199, 4194304, F4, 25) (dual of [4194304, 4194105, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- 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(413, 68, F4, 6) (dual of [68, 55, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 70, F4, 6) (dual of [70, 57, 7]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- OOA 2-folding [i] based on linear OA(4212, 4194372, F4, 25) (dual of [4194372, 4194160, 26]-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(4215, 2035933, F4, 3, 25) (dual of [(2035933, 3), 6107584, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (190, 215, 2035933)-net over F4 | [i] | ||