Information on Result #801620
Linear OA(2145, 295, F2, 37) (dual of [295, 150, 38]-code), using construction XX applied to Ce(36) ⊂ Ce(28) ⊂ Ce(26) based on
- linear OA(2125, 256, F2, 37) (dual of [256, 131, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2109, 256, F2, 29) (dual of [256, 147, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2101, 256, F2, 27) (dual of [256, 155, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(216, 35, F2, 7) (dual of [35, 19, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(216, 37, F2, 7) (dual of [37, 21, 8]-code), using
- adding a parity check bit [i] based on linear OA(215, 36, F2, 6) (dual of [36, 21, 7]-code), using
- extracting embedded orthogonal array [i] based on digital (9, 15, 36)-net over F2, using
- adding a parity check bit [i] based on linear OA(215, 36, F2, 6) (dual of [36, 21, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(216, 37, F2, 7) (dual of [37, 21, 8]-code), using
- linear OA(21, 4, F2, 1) (dual of [4, 3, 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(2144, 294, F2, 36) (dual of [294, 150, 37]-code) | [i] | Truncation | |