Information on Result #2175045
Linear OA(2144, 159, F2, 67) (dual of [159, 15, 68]-code), using adding a parity check bit based on linear OA(2143, 158, F2, 66) (dual of [158, 15, 67]-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]) [i] 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(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(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
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(2144, 159, F2, 66) (dual of [159, 15, 67]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2144, 159, F2, 65) (dual of [159, 15, 66]-code) | [i] | ||
| 3 | Linear OA(2144, 159, F2, 64) (dual of [159, 15, 65]-code) | [i] | ||
| 4 | Linear OA(2145, 160, F2, 67) (dual of [160, 15, 68]-code) | [i] | Code Embedding in Larger Space | |
| 5 | Linear OA(2142, 157, F2, 65) (dual of [157, 15, 66]-code) | [i] | Truncation | |
| 6 | Linear OA(2141, 156, F2, 64) (dual of [156, 15, 65]-code) | [i] | ||
| 7 | Linear OOA(2144, 79, F2, 2, 67) (dual of [(79, 2), 14, 68]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2144, 53, F2, 3, 67) (dual of [(53, 3), 15, 68]-NRT-code) | [i] | ||