Information on Result #1082442
Linear OOA(8177, large, F81, 4, 11), using (u, u+v)-construction based on
- linear OOA(8117, 4194301, F81, 4, 5) (dual of [(4194301, 4), 16777187, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(8117, large, F81, 5) (dual of [large, large−17, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(8117, large, F81, 5) (dual of [large, large−17, 6]-code), using
- linear OOA(8160, 4194302, F81, 4, 11) (dual of [(4194302, 4), 16777148, 12]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(8117, 4194301, F81, 4, 5) (dual of [(4194301, 4), 16777187, 6]-NRT-code) (see above)
- linear OOA(8143, 2097151, F81, 4, 11) (dual of [(2097151, 4), 8388561, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(8143, 4194302, F81, 2, 11) (dual of [(4194302, 2), 8388561, 12]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(8141, 4194301, F81, 2, 11) (dual of [(4194301, 2), 8388561, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8141, 8388602, F81, 11) (dual of [8388602, 8388561, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(8141, large, F81, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8141, large, F81, 11) (dual of [large, large−41, 12]-code), using
- OOA 2-folding [i] based on linear OA(8141, 8388602, F81, 11) (dual of [8388602, 8388561, 12]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(8141, 4194301, F81, 2, 11) (dual of [(4194301, 2), 8388561, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(8143, 4194302, F81, 2, 11) (dual of [(4194302, 2), 8388561, 12]-NRT-code), using
- (u, u+v)-construction [i] based on
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, 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(8177, large, F81, 4, 10) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(8177, large, F81, 4, 9) | [i] | ||
| 3 | Linear OOA(8177, large, F81, 4, 8) | [i] | ||
| 4 | Linear OOA(8177, large, F81, 4, 7) | [i] | ||
| 5 | Linear OOA(8177, large, F81, 4, 6) | [i] | ||
| 6 | Linear OOA(8177, large, F81, 4, 5) | [i] | ||
| 7 | Linear OOA(8177, large, F81, 4, 4) | [i] | ||
| 8 | Linear OOA(8177, large, F81, 4, 3) | [i] | ||