Information on Result #2225163
Linear OA(2151, 1064, F2, 28) (dual of [1064, 913, 29]-code), using 1 times truncation based on linear OA(2152, 1065, F2, 29) (dual of [1065, 913, 30]-code), using
- construction XX applied to C1 = C([1019,22]), C2 = C([1,24]), C3 = C1 + C2 = C([1,22]), and C∩ = C1 ∩ C2 = C([1019,24]) [i] based on
- 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 = {−4,−3,…,22}, and designed minimum distance d ≥ |I|+1 = 28 [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(2141, 1023, F2, 29) (dual of [1023, 882, 30]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,24}, and designed minimum distance d ≥ |I|+1 = 30 [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(210, 31, F2, 4) (dual of [31, 21, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(210, 32, F2, 4) (dual of [32, 22, 5]-code), using
- 1 times truncation [i] based on linear OA(211, 33, F2, 5) (dual of [33, 22, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33 | 210−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(211, 33, F2, 5) (dual of [33, 22, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(210, 32, F2, 4) (dual of [32, 22, 5]-code), 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, 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(2151, 542, F2, 2, 28) (dual of [(542, 2), 933, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2151, 542, F2, 3, 28) (dual of [(542, 3), 1475, 29]-NRT-code) | [i] | ||
| 3 | Linear OOA(2151, 542, F2, 4, 28) (dual of [(542, 4), 2017, 29]-NRT-code) | [i] | ||
| 4 | Linear OOA(2151, 542, F2, 5, 28) (dual of [(542, 5), 2559, 29]-NRT-code) | [i] | ||
| 5 | Linear OOA(2151, 542, F2, 6, 28) (dual of [(542, 6), 3101, 29]-NRT-code) | [i] | ||
| 6 | Linear OOA(2151, 542, F2, 7, 28) (dual of [(542, 7), 3643, 29]-NRT-code) | [i] | ||
| 7 | Linear OOA(2151, 542, F2, 8, 28) (dual of [(542, 8), 4185, 29]-NRT-code) | [i] | ||
| 8 | Digital (123, 151, 542)-net over F2 | [i] | ||
| 9 | Linear OOA(2151, 266, F2, 4, 28) (dual of [(266, 4), 913, 29]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(2151, 152, F2, 7, 28) (dual of [(152, 7), 913, 29]-NRT-code) | [i] | ||
| 11 | Linear OOA(2151, 133, F2, 8, 28) (dual of [(133, 8), 913, 29]-NRT-code) | [i] | ||