Information on Result #807468
Linear OOA(2153, 537, F2, 2, 29) (dual of [(537, 2), 921, 30]-NRT-code), using OOA 2-folding based on linear OA(2153, 1074, F2, 29) (dual of [1074, 921, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2153, 1075, F2, 29) (dual of [1075, 922, 30]-code), using
- construction XX applied to C1 = C([1019,20]), C2 = C([0,24]), C3 = C1 + C2 = C([0,20]), and C∩ = C1 ∩ C2 = C([1019,24]) [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 = {−4,−3,…,20}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2121, 1023, F2, 25) (dual of [1023, 902, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [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(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(26, 26, F2, 3) (dual of [26, 20, 4]-code or 26-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- linear OA(26, 26, F2, 3) (dual of [26, 20, 4]-code or 26-cap in PG(5,2)) (see above)
- construction XX applied to C1 = C([1019,20]), C2 = C([0,24]), C3 = C1 + C2 = C([0,20]), and C∩ = C1 ∩ C2 = C([1019,24]) [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(2153, 537, F2, 3, 29) (dual of [(537, 3), 1458, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2153, 537, F2, 4, 29) (dual of [(537, 4), 1995, 30]-NRT-code) | [i] | ||
| 3 | Linear OOA(2153, 537, F2, 5, 29) (dual of [(537, 5), 2532, 30]-NRT-code) | [i] | ||
| 4 | Linear OOA(2153, 537, F2, 6, 29) (dual of [(537, 6), 3069, 30]-NRT-code) | [i] | ||
| 5 | Linear OOA(2153, 537, F2, 7, 29) (dual of [(537, 7), 3606, 30]-NRT-code) | [i] | ||
| 6 | Linear OOA(2153, 537, F2, 8, 29) (dual of [(537, 8), 4143, 30]-NRT-code) | [i] | ||
| 7 | Digital (124, 153, 537)-net over F2 | [i] | ||