Information on Result #2495488
Linear OOA(4120, 131077, F4, 2, 18) (dual of [(131077, 2), 262034, 19]-NRT-code), using 41 times duplication based on linear OOA(4119, 131077, F4, 2, 18) (dual of [(131077, 2), 262035, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4119, 262154, F4, 18) (dual of [262154, 262035, 19]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4118, 262153, F4, 18) (dual of [262153, 262035, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(4118, 262144, F4, 18) (dual of [262144, 262026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(4109, 262144, F4, 17) (dual of [262144, 262035, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(40, 9, F4, 0) (dual of [9, 9, 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(17) ⊂ Ce(16) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4118, 262153, F4, 18) (dual of [262153, 262035, 19]-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(4120, 116629, F4, 3, 18) (dual of [(116629, 3), 349767, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (102, 120, 116629)-net over F4 | [i] | ||