Information on Result #2480704
Linear OOA(2212, 525, F2, 2, 43) (dual of [(525, 2), 838, 44]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2210, 524, F2, 2, 43) (dual of [(524, 2), 838, 44]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2210, 1048, F2, 43) (dual of [1048, 838, 44]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2209, 1047, F2, 43) (dual of [1047, 838, 44]-code), using
- adding a parity check bit [i] based on linear OA(2208, 1046, F2, 42) (dual of [1046, 838, 43]-code), using
- construction XX applied to C1 = C([1021,38]), C2 = C([1,40]), C3 = C1 + C2 = C([1,38]), and C∩ = C1 ∩ C2 = C([1021,40]) [i] based on
- linear OA(2196, 1023, F2, 41) (dual of [1023, 827, 42]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,38}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2195, 1023, F2, 40) (dual of [1023, 828, 41]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2206, 1023, F2, 43) (dual of [1023, 817, 44]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,40}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(2185, 1023, F2, 38) (dual of [1023, 838, 39]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [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([1021,38]), C2 = C([1,40]), C3 = C1 + C2 = C([1,38]), and C∩ = C1 ∩ C2 = C([1021,40]) [i] based on
- adding a parity check bit [i] based on linear OA(2208, 1046, F2, 42) (dual of [1046, 838, 43]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2209, 1047, F2, 43) (dual of [1047, 838, 44]-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(2212, 525, F2, 3, 43) (dual of [(525, 3), 1363, 44]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2212, 525, F2, 4, 43) (dual of [(525, 4), 1888, 44]-NRT-code) | [i] | ||
| 3 | Linear OOA(2212, 525, F2, 5, 43) (dual of [(525, 5), 2413, 44]-NRT-code) | [i] | ||
| 4 | Linear OOA(2212, 525, F2, 6, 43) (dual of [(525, 6), 2938, 44]-NRT-code) | [i] | ||
| 5 | Linear OOA(2212, 525, F2, 7, 43) (dual of [(525, 7), 3463, 44]-NRT-code) | [i] | ||
| 6 | Linear OOA(2212, 525, F2, 8, 43) (dual of [(525, 8), 3988, 44]-NRT-code) | [i] | ||
| 7 | Digital (169, 212, 525)-net over F2 | [i] | ||