Information on Result #2271872
Linear OA(4112, 16411, F4, 21) (dual of [16411, 16299, 22]-code), using 1 times code embedding in larger space based on linear OA(4111, 16410, F4, 21) (dual of [16410, 16299, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(485, 16384, F4, 17) (dual of [16384, 16299, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(45, 26, F4, 3) (dual of [26, 21, 4]-code or 26-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), 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(4112, 8683, F4, 2, 21) (dual of [(8683, 2), 17254, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4112, 8683, F4, 3, 21) (dual of [(8683, 3), 25937, 22]-NRT-code) | [i] | ||
| 3 | Digital (91, 112, 8683)-net over F4 | [i] | ||
| 4 | Linear OOA(4112, 1641, F4, 21, 21) (dual of [(1641, 21), 34349, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |