Information on Result #2495988
Linear OOA(4171, 524313, F4, 2, 22) (dual of [(524313, 2), 1048455, 23]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4169, 524312, F4, 2, 22) (dual of [(524312, 2), 1048455, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4169, 1048624, F4, 22) (dual of [1048624, 1048455, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(4161, 1048576, F4, 22) (dual of [1048576, 1048415, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(4121, 1048576, F4, 17) (dual of [1048576, 1048455, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(48, 48, F4, 4) (dual of [48, 40, 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(21) ⊂ Ce(16) [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(4172, 524313, F4, 2, 22) (dual of [(524313, 2), 1048454, 23]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(4171, 524313, F4, 3, 22) (dual of [(524313, 3), 1572768, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (149, 171, 524313)-net over F4 | [i] | ||