Information on Result #2479415
Linear OOA(2137, 525, F2, 2, 27) (dual of [(525, 2), 913, 28]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2135, 524, F2, 2, 27) (dual of [(524, 2), 913, 28]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2135, 1048, F2, 27) (dual of [1048, 913, 28]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2134, 1047, F2, 27) (dual of [1047, 913, 28]-code), using
- adding a parity check bit [i] based on linear OA(2133, 1046, F2, 26) (dual of [1046, 913, 27]-code), using
- construction XX applied to C1 = C([1021,22]), C2 = C([1,24]), C3 = C1 + C2 = C([1,22]), and C∩ = C1 ∩ C2 = C([1021,24]) [i] based on
- linear OA(2121, 1023, F2, 25) (dual of [1023, 902, 26]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,22}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2120, 1023, F2, 24) (dual of [1023, 903, 25]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(2131, 1023, F2, 27) (dual of [1023, 892, 28]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,24}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2110, 1023, F2, 22) (dual of [1023, 913, 23]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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, 11, F2, 1) (dual of [11, 10, 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([1021,22]), C2 = C([1,24]), C3 = C1 + C2 = C([1,22]), and C∩ = C1 ∩ C2 = C([1021,24]) [i] based on
- adding a parity check bit [i] based on linear OA(2133, 1046, F2, 26) (dual of [1046, 913, 27]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2134, 1047, F2, 27) (dual of [1047, 913, 28]-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(2137, 450, F2, 3, 27) (dual of [(450, 3), 1213, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2137, 450, F2, 4, 27) (dual of [(450, 4), 1663, 28]-NRT-code) | [i] | ||
| 3 | Linear OOA(2137, 450, F2, 5, 27) (dual of [(450, 5), 2113, 28]-NRT-code) | [i] | ||
| 4 | Linear OOA(2137, 450, F2, 6, 27) (dual of [(450, 6), 2563, 28]-NRT-code) | [i] | ||
| 5 | Linear OOA(2137, 450, F2, 7, 27) (dual of [(450, 7), 3013, 28]-NRT-code) | [i] | ||
| 6 | Linear OOA(2137, 450, F2, 8, 27) (dual of [(450, 8), 3463, 28]-NRT-code) | [i] | ||
| 7 | Digital (110, 137, 450)-net over F2 | [i] | ||