Information on Result #700655
Linear OA(2142, 168, F2, 56) (dual of [168, 26, 57]-code), using construction XX applied to C1 = C({0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,63}), C2 = C([1,47]), C3 = C1 + C2 = C([1,31]), 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(2106, 127, F2, 47) (dual of [127, 21, 48]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,63}, and minimum distance d ≥ |{−4,−3,…,42}|+1 = 48 (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(298, 127, F2, 42) (dual of [127, 29, 43]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(21, 9, F2, 1) (dual of [9, 8, 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
- linear OA(221, 32, F2, 11) (dual of [32, 11, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(2143, 169, F2, 57) (dual of [169, 26, 58]-code) | [i] | Adding a Parity Check Bit | |
| 2 | Linear OOA(2142, 84, F2, 2, 56) (dual of [(84, 2), 26, 57]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2142, 56, F2, 3, 56) (dual of [(56, 3), 26, 57]-NRT-code) | [i] | ||