Information on Result #2478874
Linear OOA(2107, 525, F2, 2, 21) (dual of [(525, 2), 943, 22]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2105, 524, F2, 2, 21) (dual of [(524, 2), 943, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2105, 1048, F2, 21) (dual of [1048, 943, 22]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2104, 1047, F2, 21) (dual of [1047, 943, 22]-code), using
- adding a parity check bit [i] based on linear OA(2103, 1046, F2, 20) (dual of [1046, 943, 21]-code), using
- construction XX applied to C1 = C([1021,16]), C2 = C([1,18]), C3 = C1 + C2 = C([1,16]), and C∩ = C1 ∩ C2 = C([1021,18]) [i] based on
- linear OA(291, 1023, F2, 19) (dual of [1023, 932, 20]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,16}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(290, 1023, F2, 18) (dual of [1023, 933, 19]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 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(280, 1023, F2, 16) (dual of [1023, 943, 17]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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([1021,16]), C2 = C([1,18]), C3 = C1 + C2 = C([1,16]), and C∩ = C1 ∩ C2 = C([1021,18]) [i] based on
- adding a parity check bit [i] based on linear OA(2103, 1046, F2, 20) (dual of [1046, 943, 21]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2104, 1047, F2, 21) (dual of [1047, 943, 22]-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(2107, 406, F2, 3, 21) (dual of [(406, 3), 1111, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2107, 406, F2, 4, 21) (dual of [(406, 4), 1517, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(2107, 406, F2, 5, 21) (dual of [(406, 5), 1923, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(2107, 406, F2, 6, 21) (dual of [(406, 6), 2329, 22]-NRT-code) | [i] | ||
| 5 | Linear OOA(2107, 406, F2, 7, 21) (dual of [(406, 7), 2735, 22]-NRT-code) | [i] | ||
| 6 | Linear OOA(2107, 406, F2, 8, 21) (dual of [(406, 8), 3141, 22]-NRT-code) | [i] | ||
| 7 | Digital (86, 107, 406)-net over F2 | [i] | ||