Information on Result #672843
Linear OA(2134, 4109, F2, 23) (dual of [4109, 3975, 24]-code), using construction X applied to Ce(22) ⊂ Ce(20) based on
- linear OA(2133, 4096, F2, 23) (dual of [4096, 3963, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2121, 4096, F2, 21) (dual of [4096, 3975, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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
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 OA(2134, 4109, F2, 22) (dual of [4109, 3975, 23]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2135, 4110, F2, 23) (dual of [4110, 3975, 24]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2136, 4111, F2, 23) (dual of [4111, 3975, 24]-code) | [i] | ||
| 4 | Linear OA(2137, 4112, F2, 23) (dual of [4112, 3975, 24]-code) | [i] | ||
| 5 | Linear OA(2138, 4113, F2, 23) (dual of [4113, 3975, 24]-code) | [i] | ||
| 6 | Linear OA(2133, 4108, F2, 22) (dual of [4108, 3975, 23]-code) | [i] | Truncation | |
| 7 | Linear OOA(2134, 2054, F2, 2, 23) (dual of [(2054, 2), 3974, 24]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2134, 1369, F2, 3, 23) (dual of [(1369, 3), 3973, 24]-NRT-code) | [i] | ||
| 9 | Linear OOA(2134, 1027, F2, 4, 23) (dual of [(1027, 4), 3974, 24]-NRT-code) | [i] | ||
| 10 | Linear OOA(2134, 821, F2, 5, 23) (dual of [(821, 5), 3971, 24]-NRT-code) | [i] | ||
| 11 | Linear OOA(2134, 684, F2, 6, 23) (dual of [(684, 6), 3970, 24]-NRT-code) | [i] | ||
| 12 | Linear OOA(2134, 587, F2, 7, 23) (dual of [(587, 7), 3975, 24]-NRT-code) | [i] | ||
| 13 | Linear OOA(2134, 513, F2, 8, 23) (dual of [(513, 8), 3970, 24]-NRT-code) | [i] | ||
| 14 | Linear OOA(2134, 373, F2, 23, 23) (dual of [(373, 23), 8445, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |