Information on Result #700671
Linear OA(2150, 165, F2, 70) (dual of [165, 15, 71]-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(212, 19, F2, 7) (dual of [19, 7, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(212, 24, F2, 7) (dual of [24, 12, 8]-code), using
- extended Golay code Ge(2) [i]
- discarding factors / shortening the dual code based on linear OA(212, 24, F2, 7) (dual of [24, 12, 8]-code), using
- linear OA(212, 19, F2, 7) (dual of [19, 7, 8]-code) (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(2150, 165, F2, 69) (dual of [165, 15, 70]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2150, 165, F2, 68) (dual of [165, 15, 69]-code) | [i] | ||
| 3 | Linear OA(2152, 167, F2, 70) (dual of [167, 15, 71]-code) | [i] | Code Embedding in Larger Space | |
| 4 | Linear OA(2151, 166, F2, 71) (dual of [166, 15, 72]-code) | [i] | Adding a Parity Check Bit | |
| 5 | Linear OOA(2150, 82, F2, 2, 70) (dual of [(82, 2), 14, 71]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(2150, 55, F2, 3, 70) (dual of [(55, 3), 15, 71]-NRT-code) | [i] | ||
| 7 | Linear OOA(2150, 33, F2, 5, 70) (dual of [(33, 5), 15, 71]-NRT-code) | [i] | ||