Information on Result #2480219
Linear OOA(2181, 522, F2, 2, 37) (dual of [(522, 2), 863, 38]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2179, 521, F2, 2, 37) (dual of [(521, 2), 863, 38]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2179, 1042, F2, 37) (dual of [1042, 863, 38]-code), using
- adding a parity check bit [i] based on linear OA(2178, 1041, F2, 36) (dual of [1041, 863, 37]-code), using
- construction XX applied to C1 = C([1021,32]), C2 = C([1,34]), C3 = C1 + C2 = C([1,32]), and C∩ = C1 ∩ C2 = C([1021,34]) [i] based on
- linear OA(2171, 1023, F2, 35) (dual of [1023, 852, 36]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,32}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2165, 1023, F2, 34) (dual of [1023, 858, 35]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2176, 1023, F2, 37) (dual of [1023, 847, 38]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,34}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2160, 1023, F2, 32) (dual of [1023, 863, 33]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(21, 6, F2, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)
- construction XX applied to C1 = C([1021,32]), C2 = C([1,34]), C3 = C1 + C2 = C([1,32]), and C∩ = C1 ∩ C2 = C([1021,34]) [i] based on
- adding a parity check bit [i] based on linear OA(2178, 1041, F2, 36) (dual of [1041, 863, 37]-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(2181, 473, F2, 3, 37) (dual of [(473, 3), 1238, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2181, 473, F2, 4, 37) (dual of [(473, 4), 1711, 38]-NRT-code) | [i] | ||
| 3 | Linear OOA(2181, 473, F2, 5, 37) (dual of [(473, 5), 2184, 38]-NRT-code) | [i] | ||
| 4 | Linear OOA(2181, 473, F2, 6, 37) (dual of [(473, 6), 2657, 38]-NRT-code) | [i] | ||
| 5 | Linear OOA(2181, 473, F2, 7, 37) (dual of [(473, 7), 3130, 38]-NRT-code) | [i] | ||
| 6 | Linear OOA(2181, 473, F2, 8, 37) (dual of [(473, 8), 3603, 38]-NRT-code) | [i] | ||
| 7 | Digital (144, 181, 473)-net over F2 | [i] | ||