Information on Result #2497130
Linear OOA(4256, 524320, F4, 2, 33) (dual of [(524320, 2), 1048384, 34]-NRT-code), using 41 times duplication based on linear OOA(4255, 524320, F4, 2, 33) (dual of [(524320, 2), 1048385, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4255, 1048640, F4, 33) (dual of [1048640, 1048385, 34]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4254, 1048639, F4, 33) (dual of [1048639, 1048385, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(25) [i] based on
- linear OA(4241, 1048576, F4, 33) (dual of [1048576, 1048335, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(4191, 1048576, F4, 26) (dual of [1048576, 1048385, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- construction X applied to Ce(32) ⊂ Ce(25) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4254, 1048639, F4, 33) (dual of [1048639, 1048385, 34]-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(4256, 502444, F4, 3, 33) (dual of [(502444, 3), 1507076, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (223, 256, 502444)-net over F4 | [i] | ||