Information on Result #700679
Linear OA(2138, 151, F2, 64) (dual of [151, 13, 65]-code), using construction XX applied to C1 = C({1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,47,63}), C2 = C([1,55]), C3 = C1 + C2 = C([1,47]), and C∩ = C1 ∩ C2 = C([1,63]) based on
- linear OA(2119, 127, F2, 62) (dual of [127, 8, 63]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,47,63}, and minimum distance d ≥ |{9,18,27,…,50}|+1 = 63 (BCH-bound) [i]
- linear OA(2119, 127, F2, 62) (dual of [127, 8, 63]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,55], and designed minimum distance d ≥ |I|+1 = 63 [i]
- linear OA(2126, 127, F2, 126) (dual of [127, 1, 127]-code or 127-arc in PG(125,2)), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,63], and designed minimum distance d ≥ |I|+1 = 127 [i]
- linear OA(2112, 127, F2, 54) (dual of [127, 15, 55]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,47], and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(211, 16, F2, 7) (dual of [16, 5, 8]-code), using
- Reed–Muller code RM(2,4) [i]
- linear OA(21, 8, F2, 1) (dual of [8, 7, 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.
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(2139, 152, F2, 65) (dual of [152, 13, 66]-code) | [i] | Adding a Parity Check Bit | |
| 2 | Linear OOA(2138, 75, F2, 2, 64) (dual of [(75, 2), 12, 65]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2138, 50, F2, 3, 64) (dual of [(50, 3), 12, 65]-NRT-code) | [i] | ||
| 4 | Linear OOA(2138, 30, F2, 5, 64) (dual of [(30, 5), 12, 65]-NRT-code) | [i] | ||