Information on Result #822903
Linear OOA(4100, 2097158, F4, 2, 12) (dual of [(2097158, 2), 4194216, 13]-NRT-code), using OOA 2-folding based on linear OA(4100, 4194316, F4, 12) (dual of [4194316, 4194216, 13]-code), using
- construction X4 applied to C([1,12]) ⊂ C([1,10]) [i] based on
- linear OA(499, 4194303, F4, 12) (dual of [4194303, 4194204, 13]-code), using the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(488, 4194303, F4, 10) (dual of [4194303, 4194215, 11]-code), using the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(412, 13, F4, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,4)), using
- dual of repetition code with length 13 [i]
- linear OA(41, 13, F4, 1) (dual of [13, 12, 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(4100, 2097158, F4, 3, 12) (dual of [(2097158, 3), 6291374, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (88, 100, 2097158)-net over F4 | [i] | ||