Information on Result #2616902
Linear OOA(2213, 1376, F2, 3, 34) (dual of [(1376, 3), 3915, 35]-NRT-code), using strength reduction based on linear OOA(2213, 1376, F2, 3, 35) (dual of [(1376, 3), 3915, 36]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2213, 4128, F2, 35) (dual of [4128, 3915, 36]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2211, 4126, F2, 35) (dual of [4126, 3915, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(30) [i] based on
- linear OA(2205, 4096, F2, 35) (dual of [4096, 3891, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2181, 4096, F2, 31) (dual of [4096, 3915, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(26, 30, F2, 3) (dual of [30, 24, 4]-code or 30-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
- construction X applied to Ce(34) ⊂ Ce(30) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(2211, 4126, F2, 35) (dual of [4126, 3915, 36]-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(2214, 1376, F2, 3, 34) (dual of [(1376, 3), 3914, 35]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2215, 1376, F2, 3, 34) (dual of [(1376, 3), 3913, 35]-NRT-code) | [i] | ||
| 3 | Linear OOA(2213, 1376, F2, 4, 34) (dual of [(1376, 4), 5291, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2213, 1376, F2, 5, 34) (dual of [(1376, 5), 6667, 35]-NRT-code) | [i] | ||
| 5 | Linear OOA(2213, 1376, F2, 6, 34) (dual of [(1376, 6), 8043, 35]-NRT-code) | [i] | ||
| 6 | Linear OOA(2213, 1376, F2, 7, 34) (dual of [(1376, 7), 9419, 35]-NRT-code) | [i] | ||
| 7 | Linear OOA(2213, 1376, F2, 8, 34) (dual of [(1376, 8), 10795, 35]-NRT-code) | [i] | ||
| 8 | Digital (179, 213, 1376)-net over F2 | [i] | ||