Information on Result #806653
Linear OOA(2112, 522, F2, 2, 22) (dual of [(522, 2), 932, 23]-NRT-code), using OOA 2-folding based on linear OA(2112, 1044, F2, 22) (dual of [1044, 932, 23]-code), using
- 1 times truncation [i] based on linear OA(2113, 1045, F2, 23) (dual of [1045, 932, 24]-code), using
- construction XX applied to C1 = C([1021,18]), C2 = C([0,20]), C3 = C1 + C2 = C([0,18]), and C∩ = C1 ∩ C2 = C([1021,20]) [i] based on
- linear OA(2101, 1023, F2, 21) (dual of [1023, 922, 22]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,18}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2101, 1023, F2, 21) (dual of [1023, 922, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2111, 1023, F2, 23) (dual of [1023, 912, 24]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,20}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(291, 1023, F2, 19) (dual of [1023, 932, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- 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
- linear OA(21, 11, F2, 1) (dual of [11, 10, 2]-code) (see above)
- construction XX applied to C1 = C([1021,18]), C2 = C([0,20]), C3 = C1 + C2 = C([0,18]), and C∩ = C1 ∩ C2 = C([1021,20]) [i] based on
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(2112, 412, F2, 3, 22) (dual of [(412, 3), 1124, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2112, 412, F2, 4, 22) (dual of [(412, 4), 1536, 23]-NRT-code) | [i] | ||
| 3 | Linear OOA(2112, 412, F2, 5, 22) (dual of [(412, 5), 1948, 23]-NRT-code) | [i] | ||
| 4 | Linear OOA(2112, 412, F2, 6, 22) (dual of [(412, 6), 2360, 23]-NRT-code) | [i] | ||
| 5 | Linear OOA(2112, 412, F2, 7, 22) (dual of [(412, 7), 2772, 23]-NRT-code) | [i] | ||
| 6 | Linear OOA(2112, 412, F2, 8, 22) (dual of [(412, 8), 3184, 23]-NRT-code) | [i] | ||
| 7 | Digital (90, 112, 412)-net over F2 | [i] | ||