Information on Result #700657
Linear OA(2140, 162, F2, 59) (dual of [162, 22, 60]-code), using construction XX applied to C1 = C({0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,63}), C2 = C([1,47]), C3 = C1 + C2 = C([1,43]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,47,63}) based on
- 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(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(2120, 127, F2, 63) (dual of [127, 7, 64]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,47,63}, and minimum distance d ≥ |{0,9,18,…,50}|+1 = 64 (BCH-bound) [i]
- linear OA(2105, 127, F2, 46) (dual of [127, 22, 47]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(28, 16, F2, 4) (dual of [16, 8, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(28, 17, F2, 4) (dual of [17, 9, 5]-code), using
- 1 times truncation [i] based on linear OA(29, 18, F2, 5) (dual of [18, 9, 6]-code), using
- extended quadratic residue code Qe(18,2) [i]
- 1 times truncation [i] based on linear OA(29, 18, F2, 5) (dual of [18, 9, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(28, 17, F2, 4) (dual of [17, 9, 5]-code), 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(2140, 162, F2, 58) (dual of [162, 22, 59]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2139, 161, F2, 58) (dual of [161, 22, 59]-code) | [i] | Truncation | |
| 3 | Linear OOA(2140, 54, F2, 3, 59) (dual of [(54, 3), 22, 60]-NRT-code) | [i] | OOA Folding | |