Information on Result #1466373
Linear OOA(3188, 4194367, F3, 2, 17) (dual of [(4194367, 2), 8388546, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(322, 66, F3, 2, 8) (dual of [(66, 2), 110, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(322, 66, F3, 8) (dual of [66, 44, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(322, 89, F3, 8) (dual of [89, 67, 9]-code), using
- construction XX applied to C1 = C({0,1,2,4,53}), C2 = C([0,5]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C({0,1,2,4,5,53}) [i] based on
- linear OA(317, 80, F3, 6) (dual of [80, 63, 7]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,53}, and minimum distance d ≥ |{−1,0,…,4}|+1 = 7 (BCH-bound) [i]
- linear OA(317, 80, F3, 7) (dual of [80, 63, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(321, 80, F3, 8) (dual of [80, 59, 9]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,5,53}, and minimum distance d ≥ |{−1,0,…,6}|+1 = 9 (BCH-bound) [i]
- linear OA(313, 80, F3, 5) (dual of [80, 67, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(30, 4, F3, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(31, 5, F3, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction XX applied to C1 = C({0,1,2,4,53}), C2 = C([0,5]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C({0,1,2,4,5,53}) [i] based on
- discarding factors / shortening the dual code based on linear OA(322, 89, F3, 8) (dual of [89, 67, 9]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(322, 66, F3, 8) (dual of [66, 44, 9]-code), using
- linear OOA(3166, 4194301, F3, 2, 17) (dual of [(4194301, 2), 8388436, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3166, 8388602, F3, 17) (dual of [8388602, 8388436, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3166, large, F3, 17) (dual of [large, large−166, 18]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(3166, large, F3, 17) (dual of [large, large−166, 18]-code), using
- OOA 2-folding [i] based on linear OA(3166, 8388602, F3, 17) (dual of [8388602, 8388436, 18]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(3188, 4194367, F3, 3, 17) (dual of [(4194367, 3), 12582913, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3188, 4194367, F3, 4, 17) (dual of [(4194367, 4), 16777280, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(3188, 4194367, F3, 5, 17) (dual of [(4194367, 5), 20971647, 18]-NRT-code) | [i] | ||
| 4 | Digital (171, 188, 4194367)-net over F3 | [i] | ||