Information on Result #2273169
Linear OA(4258, 262212, F4, 36) (dual of [262212, 261954, 37]-code), using 1 times code embedding in larger space based on linear OA(4257, 262211, F4, 36) (dual of [262211, 261954, 37]-code), using
- construction X applied to Ce(36) ⊂ Ce(28) [i] based on
- linear OA(4244, 262144, F4, 37) (dual of [262144, 261900, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(4190, 262144, F4, 29) (dual of [262144, 261954, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(413, 67, F4, 6) (dual of [67, 54, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(413, 64, F4, 6) (dual of [64, 51, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(410, 64, F4, 5) (dual of [64, 54, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
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(4258, 160378, F4, 2, 36) (dual of [(160378, 2), 320498, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4258, 160378, F4, 3, 36) (dual of [(160378, 3), 480876, 37]-NRT-code) | [i] | ||
| 3 | Digital (222, 258, 160378)-net over F4 | [i] | ||
| 4 | Linear OOA(4258, 131106, F4, 2, 36) (dual of [(131106, 2), 261954, 37]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4258, 87404, F4, 3, 36) (dual of [(87404, 3), 261954, 37]-NRT-code) | [i] | ||