Information on Result #674038
Linear OA(2140, 156, F2, 63) (dual of [156, 16, 64]-code), using construction XX applied to Ce(62) ⊂ Ce(54) ⊂ Ce(46) based on
- linear OA(2120, 128, F2, 63) (dual of [128, 8, 64]-code), using an extension Ce(62) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,62], and designed minimum distance d ≥ |I|+1 = 63 [i]
- linear OA(2113, 128, F2, 55) (dual of [128, 15, 56]-code), using an extension Ce(54) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,54], and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(2106, 128, F2, 47) (dual of [128, 22, 48]-code), using an extension Ce(46) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(212, 20, F2, 7) (dual of [20, 8, 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(27, 8, F2, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,2)), using
- dual of repetition code with length 8 [i]
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(2142, 158, F2, 63) (dual of [158, 16, 64]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2143, 159, F2, 63) (dual of [159, 16, 64]-code) | [i] | ||
| 3 | Linear OA(2139, 155, F2, 62) (dual of [155, 16, 63]-code) | [i] | Truncation | |
| 4 | Linear OOA(2140, 78, F2, 2, 63) (dual of [(78, 2), 16, 64]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2140, 52, F2, 3, 63) (dual of [(52, 3), 16, 64]-NRT-code) | [i] | ||