Information on Result #2421726
Linear OOA(2165, 524, F2, 2, 32) (dual of [(524, 2), 883, 33]-NRT-code), using strength reduction based on linear OOA(2165, 524, F2, 2, 33) (dual of [(524, 2), 883, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2165, 1048, F2, 33) (dual of [1048, 883, 34]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2164, 1047, F2, 33) (dual of [1047, 883, 34]-code), using
- adding a parity check bit [i] based on linear OA(2163, 1046, F2, 32) (dual of [1046, 883, 33]-code), using
- construction XX applied to C1 = C([1021,28]), C2 = C([1,30]), C3 = C1 + C2 = C([1,28]), and C∩ = C1 ∩ C2 = C([1021,30]) [i] based on
- linear OA(2151, 1023, F2, 31) (dual of [1023, 872, 32]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,28}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2150, 1023, F2, 30) (dual of [1023, 873, 31]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2161, 1023, F2, 33) (dual of [1023, 862, 34]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,30}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(2140, 1023, F2, 28) (dual of [1023, 883, 29]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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([1021,28]), C2 = C([1,30]), C3 = C1 + C2 = C([1,28]), and C∩ = C1 ∩ C2 = C([1021,30]) [i] based on
- adding a parity check bit [i] based on linear OA(2163, 1046, F2, 32) (dual of [1046, 883, 33]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2164, 1047, F2, 33) (dual of [1047, 883, 34]-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(2165, 524, F2, 3, 32) (dual of [(524, 3), 1407, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2165, 524, F2, 4, 32) (dual of [(524, 4), 1931, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(2165, 524, F2, 5, 32) (dual of [(524, 5), 2455, 33]-NRT-code) | [i] | ||
| 4 | Linear OOA(2165, 524, F2, 6, 32) (dual of [(524, 6), 2979, 33]-NRT-code) | [i] | ||
| 5 | Linear OOA(2165, 524, F2, 7, 32) (dual of [(524, 7), 3503, 33]-NRT-code) | [i] | ||
| 6 | Linear OOA(2165, 524, F2, 8, 32) (dual of [(524, 8), 4027, 33]-NRT-code) | [i] | ||
| 7 | Digital (133, 165, 524)-net over F2 | [i] | ||