Information on Result #2496526
Linear OOA(4205, 524300, F4, 2, 27) (dual of [(524300, 2), 1048395, 28]-NRT-code), using 41 times duplication based on linear OOA(4204, 524300, F4, 2, 27) (dual of [(524300, 2), 1048396, 28]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4202, 524299, F4, 2, 27) (dual of [(524299, 2), 1048396, 28]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4202, 1048598, F4, 27) (dual of [1048598, 1048396, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- linear OA(4201, 1048577, F4, 27) (dual of [1048577, 1048376, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(4181, 1048577, F4, 25) (dual of [1048577, 1048396, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(41, 21, F4, 1) (dual of [21, 20, 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
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- OOA 2-folding [i] based on linear OA(4202, 1048598, F4, 27) (dual of [1048598, 1048396, 28]-code), 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(4205, 404245, F4, 3, 27) (dual of [(404245, 3), 1212530, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (178, 205, 404245)-net over F4 | [i] | ||