Information on Result #801611
Linear OA(2193, 4144, F2, 31) (dual of [4144, 3951, 32]-code), using construction X applied to Ce(30) ⊂ Ce(24) based on
- 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(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(212, 48, F2, 5) (dual of [48, 36, 6]-code), using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- extracting embedded orthogonal array [i] based on digital (7, 11, 47)-net over F2, using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-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 OA(2193, 4144, F2, 30) (dual of [4144, 3951, 31]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2195, 4146, F2, 31) (dual of [4146, 3951, 32]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2192, 4143, F2, 30) (dual of [4143, 3951, 31]-code) | [i] | Truncation | |
| 4 | Linear OOA(2193, 2072, F2, 2, 31) (dual of [(2072, 2), 3951, 32]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2193, 1381, F2, 3, 31) (dual of [(1381, 3), 3950, 32]-NRT-code) | [i] | ||
| 6 | Linear OOA(2193, 1036, F2, 4, 31) (dual of [(1036, 4), 3951, 32]-NRT-code) | [i] | ||
| 7 | Linear OOA(2193, 592, F2, 7, 31) (dual of [(592, 7), 3951, 32]-NRT-code) | [i] | ||
| 8 | Linear OOA(2193, 518, F2, 8, 31) (dual of [(518, 8), 3951, 32]-NRT-code) | [i] | ||