Information on Result #678648
Linear OA(4242, 65553, F4, 40) (dual of [65553, 65311, 41]-code), using construction X applied to Ce(40) ⊂ Ce(37) based on
- linear OA(4241, 65536, F4, 41) (dual of [65536, 65295, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(4225, 65536, F4, 38) (dual of [65536, 65311, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(41, 17, F4, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(4242, 32931, F4, 2, 40) (dual of [(32931, 2), 65620, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4242, 32931, F4, 3, 40) (dual of [(32931, 3), 98551, 41]-NRT-code) | [i] | ||
| 3 | Digital (202, 242, 32931)-net over F4 | [i] | ||
| 4 | Linear OOA(4242, 32776, F4, 2, 40) (dual of [(32776, 2), 65310, 41]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4242, 21851, F4, 3, 40) (dual of [(21851, 3), 65311, 41]-NRT-code) | [i] | ||