Information on Result #680011
Linear OA(473, 4121, F4, 15) (dual of [4121, 4048, 16]-code), using construction XX applied to Ce(14) ⊂ Ce(10) ⊂ Ce(9) based on
- linear OA(467, 4096, F4, 15) (dual of [4096, 4029, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(449, 4096, F4, 11) (dual of [4096, 4047, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(443, 4096, F4, 10) (dual of [4096, 4053, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(45, 24, F4, 3) (dual of [24, 19, 4]-code or 24-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
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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(473, 4071, F4, 2, 15) (dual of [(4071, 2), 8069, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(473, 4071, F4, 3, 15) (dual of [(4071, 3), 12140, 16]-NRT-code) | [i] | ||
| 3 | Digital (58, 73, 4071)-net over F4 | [i] | ||
| 4 | Linear OOA(473, 2060, F4, 2, 15) (dual of [(2060, 2), 4047, 16]-NRT-code) | [i] | OOA Folding | |