Information on Result #700645
Linear OA(2123, 151, F2, 51) (dual of [151, 28, 52]-code), using construction XX applied to C1 = C({0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,63}), C2 = C([0,43]), C3 = C1 + C2 = C([0,31]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,63}) based on
- linear OA(2106, 127, F2, 47) (dual of [127, 21, 48]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,63}, and minimum distance d ≥ |{−4,−3,…,42}|+1 = 48 (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(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(299, 127, F2, 43) (dual of [127, 28, 44]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(25, 12, F2, 3) (dual of [12, 7, 4]-code or 12-cap in PG(4,2)), using
- discarding factors / shortening the dual code based on linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), using
- linear OA(25, 12, F2, 3) (dual of [12, 7, 4]-code or 12-cap in PG(4,2)) (see above)
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(2122, 150, F2, 50) (dual of [150, 28, 51]-code) | [i] | Truncation | |
| 2 | Linear OOA(2123, 75, F2, 2, 51) (dual of [(75, 2), 27, 52]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2123, 50, F2, 3, 51) (dual of [(50, 3), 27, 52]-NRT-code) | [i] | ||
| 4 | Linear OOA(2123, 30, F2, 5, 51) (dual of [(30, 5), 27, 52]-NRT-code) | [i] | ||