Information on Result #679135
Linear OA(4114, 16407, F4, 20) (dual of [16407, 16293, 21]-code), using construction X4 applied to Ce(21) ⊂ Ce(17) based on
- linear OA(4113, 16384, F4, 22) (dual of [16384, 16271, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(492, 16384, F4, 18) (dual of [16384, 16292, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(422, 23, F4, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,4)), using
- dual of repetition code with length 23 [i]
- linear OA(41, 23, F4, 1) (dual of [23, 22, 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(4114, 15143, F4, 2, 20) (dual of [(15143, 2), 30172, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4114, 15143, F4, 3, 20) (dual of [(15143, 3), 45315, 21]-NRT-code) | [i] | ||
| 3 | Digital (94, 114, 15143)-net over F4 | [i] | ||