Information on Result #1682516
Linear OOA(2160, 1242, F2, 7, 26) (dual of [(1242, 7), 8534, 27]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2160, 1242, F2, 3, 26) (dual of [(1242, 3), 3566, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2160, 1370, F2, 3, 26) (dual of [(1370, 3), 3950, 27]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2159, 1370, F2, 3, 26) (dual of [(1370, 3), 3951, 27]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2159, 4110, F2, 26) (dual of [4110, 3951, 27]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2157, 4108, F2, 26) (dual of [4108, 3951, 27]-code), using
- 1 times truncation [i] based on linear OA(2158, 4109, F2, 27) (dual of [4109, 3951, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- linear OA(2157, 4096, F2, 27) (dual of [4096, 3939, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2145, 4096, F2, 25) (dual of [4096, 3951, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(26) ⊂ Ce(24) [i] based on
- 1 times truncation [i] based on linear OA(2158, 4109, F2, 27) (dual of [4109, 3951, 28]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2157, 4108, F2, 26) (dual of [4108, 3951, 27]-code), using
- OOA 3-folding [i] based on linear OA(2159, 4110, F2, 26) (dual of [4110, 3951, 27]-code), using
- 21 times duplication [i] based on linear OOA(2159, 1370, F2, 3, 26) (dual of [(1370, 3), 3951, 27]-NRT-code), using
Mode: 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(2160, 620, F2, 35, 26) (dual of [(620, 35), 21540, 27]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |