Information on Result #2666950
Linear OOA(2100, 1370, F2, 3, 16) (dual of [(1370, 3), 4010, 17]-NRT-code), using 21 times duplication based on linear OOA(299, 1370, F2, 3, 16) (dual of [(1370, 3), 4011, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(299, 4110, F2, 16) (dual of [4110, 4011, 17]-code), using
- 2 times code embedding in larger space [i] based on linear OA(297, 4108, F2, 16) (dual of [4108, 4011, 17]-code), using
- 1 times truncation [i] based on linear OA(298, 4109, F2, 17) (dual of [4109, 4011, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(14) [i] based on
- linear OA(297, 4096, F2, 17) (dual of [4096, 3999, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(285, 4096, F2, 15) (dual of [4096, 4011, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(21, 13, F2, 1) (dual of [13, 12, 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
- construction X applied to Ce(16) ⊂ Ce(14) [i] based on
- 1 times truncation [i] based on linear OA(298, 4109, F2, 17) (dual of [4109, 4011, 18]-code), using
- 2 times code embedding in larger space [i] based on linear OA(297, 4108, F2, 16) (dual of [4108, 4011, 17]-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(2100, 1370, F2, 4, 16) (dual of [(1370, 4), 5380, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2100, 1370, F2, 5, 16) (dual of [(1370, 5), 6750, 17]-NRT-code) | [i] | ||
| 3 | Linear OOA(2100, 1370, F2, 6, 16) (dual of [(1370, 6), 8120, 17]-NRT-code) | [i] | ||
| 4 | Linear OOA(2100, 1370, F2, 7, 16) (dual of [(1370, 7), 9490, 17]-NRT-code) | [i] | ||
| 5 | Linear OOA(2100, 1370, F2, 8, 16) (dual of [(1370, 8), 10860, 17]-NRT-code) | [i] | ||
| 6 | Digital (84, 100, 1370)-net over F2 | [i] | ||