Information on Result #2266246
Linear OA(3153, 2228, F3, 30) (dual of [2228, 2075, 31]-code), using 4 times code embedding in larger space based on linear OA(3149, 2224, F3, 30) (dual of [2224, 2075, 31]-code), using
- construction X applied to C([0,15]) ⊂ C([0,12]) [i] based on
- linear OA(3141, 2188, F3, 31) (dual of [2188, 2047, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(3113, 2188, F3, 25) (dual of [2188, 2075, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(38, 36, F3, 4) (dual of [36, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-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(3153, 2172, F3, 2, 30) (dual of [(2172, 2), 4191, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3153, 2172, F3, 3, 30) (dual of [(2172, 3), 6363, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(3153, 2172, F3, 4, 30) (dual of [(2172, 4), 8535, 31]-NRT-code) | [i] | ||
| 4 | Linear OOA(3153, 2172, F3, 5, 30) (dual of [(2172, 5), 10707, 31]-NRT-code) | [i] | ||
| 5 | Digital (123, 153, 2172)-net over F3 | [i] | ||