Information on Result #2480393
Linear OOA(2191, 524, F2, 2, 39) (dual of [(524, 2), 857, 40]-NRT-code), using 21 times duplication based on linear OOA(2190, 524, F2, 2, 39) (dual of [(524, 2), 858, 40]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2190, 1048, F2, 39) (dual of [1048, 858, 40]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2189, 1047, F2, 39) (dual of [1047, 858, 40]-code), using
- adding a parity check bit [i] based on linear OA(2188, 1046, F2, 38) (dual of [1046, 858, 39]-code), using
- construction XX applied to C1 = C([1021,34]), C2 = C([1,36]), C3 = C1 + C2 = C([1,34]), and C∩ = C1 ∩ C2 = C([1021,36]) [i] based on
- linear OA(2176, 1023, F2, 37) (dual of [1023, 847, 38]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,34}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2175, 1023, F2, 36) (dual of [1023, 848, 37]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2186, 1023, F2, 39) (dual of [1023, 837, 40]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,36}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2165, 1023, F2, 34) (dual of [1023, 858, 35]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [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([1021,34]), C2 = C([1,36]), C3 = C1 + C2 = C([1,34]), and C∩ = C1 ∩ C2 = C([1021,36]) [i] based on
- adding a parity check bit [i] based on linear OA(2188, 1046, F2, 38) (dual of [1046, 858, 39]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2189, 1047, F2, 39) (dual of [1047, 858, 40]-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(2191, 493, F2, 3, 39) (dual of [(493, 3), 1288, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2191, 493, F2, 4, 39) (dual of [(493, 4), 1781, 40]-NRT-code) | [i] | ||
| 3 | Linear OOA(2191, 493, F2, 5, 39) (dual of [(493, 5), 2274, 40]-NRT-code) | [i] | ||
| 4 | Linear OOA(2191, 493, F2, 6, 39) (dual of [(493, 6), 2767, 40]-NRT-code) | [i] | ||
| 5 | Linear OOA(2191, 493, F2, 7, 39) (dual of [(493, 7), 3260, 40]-NRT-code) | [i] | ||
| 6 | Linear OOA(2191, 493, F2, 8, 39) (dual of [(493, 8), 3753, 40]-NRT-code) | [i] | ||
| 7 | Digital (152, 191, 493)-net over F2 | [i] | ||