Information on Result #1117818
Linear OOA(3226, 1678271, F3, 5, 19) (dual of [(1678271, 5), 8391129, 20]-NRT-code), using (u, u+v)-construction based on
- linear OOA(345, 551, F3, 5, 9) (dual of [(551, 5), 2710, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(345, 2205, F3, 9) (dual of [2205, 2160, 10]-code), using
- 1 times code embedding in larger space [i] based on linear OA(344, 2204, F3, 9) (dual of [2204, 2160, 10]-code), using
- construction X4 applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(343, 2188, F3, 9) (dual of [2188, 2145, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(329, 2188, F3, 7) (dual of [2188, 2159, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(315, 16, F3, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,3)), using
- dual of repetition code with length 16 [i]
- linear OA(31, 16, F3, 1) (dual of [16, 15, 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 X4 applied to C([0,4]) ⊂ C([0,3]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(344, 2204, F3, 9) (dual of [2204, 2160, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(345, 2205, F3, 9) (dual of [2205, 2160, 10]-code), using
- linear OOA(3181, 1677720, F3, 5, 19) (dual of [(1677720, 5), 8388419, 20]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3181, 8388600, F3, 19) (dual of [8388600, 8388419, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- OOA 5-folding [i] based on linear OA(3181, 8388600, F3, 19) (dual of [8388600, 8388419, 20]-code), using
Mode: Constructive and 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(3226, 1678271, F3, 5, 18) (dual of [(1678271, 5), 8391129, 19]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(3227, 1678271, F3, 5, 19) (dual of [(1678271, 5), 8391128, 20]-NRT-code) | [i] | OOA Duplication | |