Information on Result #700582
Linear OA(252, 144, F2, 14) (dual of [144, 92, 15]-code), using construction XX applied to C1 = C({0,1,3,5,7,9,63}), C2 = C([1,11]), C3 = C1 + C2 = C([1,9]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,11,63}) based on
- linear OA(243, 127, F2, 13) (dual of [127, 84, 14]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,63}, and minimum distance d ≥ |{−2,−1,…,10}|+1 = 14 (BCH-bound) [i]
- linear OA(242, 127, F2, 12) (dual of [127, 85, 13]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(250, 127, F2, 15) (dual of [127, 77, 16]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,63}, and minimum distance d ≥ |{−2,−1,…,12}|+1 = 16 (BCH-bound) [i]
- linear OA(235, 127, F2, 10) (dual of [127, 92, 11]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 11 [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(21, 8, F2, 1) (dual of [8, 7, 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 (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(253, 145, F2, 15) (dual of [145, 92, 16]-code) | [i] | Adding a Parity Check Bit | |
| 2 | Linear OOA(252, 72, F2, 2, 14) (dual of [(72, 2), 92, 15]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(252, 48, F2, 3, 14) (dual of [(48, 3), 92, 15]-NRT-code) | [i] | ||