Information on Result #700668
Linear OA(2150, 171, F2, 62) (dual of [171, 21, 63]-code), using construction XX applied to C1 = C({0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,63}), C2 = C([0,47]), C3 = C1 + C2 = C([0,43]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,47,63}) based on
- linear OA(2113, 127, F2, 51) (dual of [127, 14, 52]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,63}, and minimum distance d ≥ |{−4,−3,…,46}|+1 = 52 (BCH-bound) [i]
- linear OA(2113, 127, F2, 55) (dual of [127, 14, 56]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,47], and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(2120, 127, F2, 63) (dual of [127, 7, 64]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,47,63}, and minimum distance d ≥ |{0,9,18,…,50}|+1 = 64 (BCH-bound) [i]
- linear OA(2106, 127, F2, 47) (dual of [127, 21, 48]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,43], and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(211, 18, F2, 6) (dual of [18, 7, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(211, 23, F2, 6) (dual of [23, 12, 7]-code), using
- Golay code G(2) [i]
- discarding factors / shortening the dual code based on linear OA(211, 23, F2, 6) (dual of [23, 12, 7]-code), using
- linear OA(219, 26, F2, 10) (dual of [26, 7, 11]-code), using
- 1 times truncation [i] based on linear OA(220, 27, F2, 11) (dual of [27, 7, 12]-code), using
- residual code [i] based on linear OA(243, 51, F2, 23) (dual of [51, 8, 24]-code), using
- concatenation of two codes [i] based on
- residual code [i] based on linear OA(243, 51, F2, 23) (dual of [51, 8, 24]-code), using
- 1 times truncation [i] based on linear OA(220, 27, F2, 11) (dual of [27, 7, 12]-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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(2151, 172, F2, 63) (dual of [172, 21, 64]-code) | [i] | Adding a Parity Check Bit | |
| 2 | Linear OOA(2150, 57, F2, 3, 62) (dual of [(57, 3), 21, 63]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2150, 34, F2, 5, 62) (dual of [(34, 5), 20, 63]-NRT-code) | [i] | ||