Information on Result #825030
Linear OOA(4241, 524318, F4, 2, 31) (dual of [(524318, 2), 1048395, 32]-NRT-code), using OOA 2-folding based on linear OA(4241, 1048636, F4, 31) (dual of [1048636, 1048395, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(24) [i] based on
- linear OA(4231, 1048576, F4, 31) (dual of [1048576, 1048345, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(4181, 1048576, F4, 25) (dual of [1048576, 1048395, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(410, 60, F4, 5) (dual of [60, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-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(4243, 524319, F4, 2, 31) (dual of [(524319, 2), 1048395, 32]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(4245, 524320, F4, 2, 31) (dual of [(524320, 2), 1048395, 32]-NRT-code) | [i] | ||
| 3 | Linear OOA(4242, 524318, F4, 2, 31) (dual of [(524318, 2), 1048394, 32]-NRT-code) | [i] | OOA Duplication | |
| 4 | Linear OOA(4241, 518653, F4, 3, 31) (dual of [(518653, 3), 1555718, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (210, 241, 518653)-net over F4 | [i] | ||