Information on Result #678736
Linear OA(4144, 65575, F4, 23) (dual of [65575, 65431, 24]-code), using construction X applied to Ce(22) ⊂ Ce(17) based on
- linear OA(4137, 65536, F4, 23) (dual of [65536, 65399, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(4105, 65536, F4, 18) (dual of [65536, 65431, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(4145, 65576, F4, 23) (dual of [65576, 65431, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4146, 65577, F4, 23) (dual of [65577, 65431, 24]-code) | [i] | ||
| 3 | Linear OOA(4144, 36385, F4, 2, 23) (dual of [(36385, 2), 72626, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(4144, 36385, F4, 3, 23) (dual of [(36385, 3), 109011, 24]-NRT-code) | [i] | ||
| 5 | Digital (121, 144, 36385)-net over F4 | [i] | ||
| 6 | Linear OOA(4144, 32787, F4, 2, 23) (dual of [(32787, 2), 65430, 24]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4144, 21858, F4, 3, 23) (dual of [(21858, 3), 65430, 24]-NRT-code) | [i] | ||
| 8 | Linear OOA(4144, 5961, F4, 23, 23) (dual of [(5961, 23), 136959, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |