Information on Result #730950
Linear OA(472, 518, F4, 20) (dual of [518, 446, 21]-code), using trace code based on linear OA(1636, 259, F16, 20) (dual of [259, 223, 21]-code), using
- construction XX applied to C1 = C([254,17]), C2 = C([0,18]), C3 = C1 + C2 = C([0,17]), and C∩ = C1 ∩ C2 = C([254,18]) [i] based on
- linear OA(1634, 255, F16, 19) (dual of [255, 221, 20]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−1,0,…,17}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1634, 255, F16, 19) (dual of [255, 221, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1636, 255, F16, 20) (dual of [255, 219, 21]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−1,0,…,18}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(1632, 255, F16, 18) (dual of [255, 223, 19]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(160, 2, F16, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(160, 2, F16, 0) (dual of [2, 2, 1]-code) (see above)
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 OA(473, 519, F4, 20) (dual of [519, 446, 21]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(472, 518, F4, 2, 20) (dual of [(518, 2), 964, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(472, 518, F4, 3, 20) (dual of [(518, 3), 1482, 21]-NRT-code) | [i] | ||
| 4 | Digital (52, 72, 518)-net over F4 | [i] | ||
| 5 | Linear OA(473, 554, F4, 20) (dual of [554, 481, 21]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OOA(472, 259, F4, 2, 20) (dual of [(259, 2), 446, 21]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(472, 172, F4, 3, 20) (dual of [(172, 3), 444, 21]-NRT-code) | [i] | ||