Information on Result #678728
Linear OA(4216, 65575, F4, 35) (dual of [65575, 65359, 36]-code), using construction X applied to Ce(34) ⊂ Ce(29) based on
- linear OA(4209, 65536, F4, 35) (dual of [65536, 65327, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(4177, 65536, F4, 30) (dual of [65536, 65359, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(47, 39, F4, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-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 OA(4217, 65576, F4, 35) (dual of [65576, 65359, 36]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4218, 65577, F4, 35) (dual of [65577, 65359, 36]-code) | [i] | ||
| 3 | Linear OOA(4216, 36680, F4, 2, 35) (dual of [(36680, 2), 73144, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(4216, 36680, F4, 3, 35) (dual of [(36680, 3), 109824, 36]-NRT-code) | [i] | ||
| 5 | Digital (181, 216, 36680)-net over F4 | [i] | ||
| 6 | Linear OOA(4216, 32787, F4, 2, 35) (dual of [(32787, 2), 65358, 36]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4216, 21858, F4, 3, 35) (dual of [(21858, 3), 65358, 36]-NRT-code) | [i] | ||
| 8 | Linear OOA(4216, 3857, F4, 35, 35) (dual of [(3857, 35), 134779, 36]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |