Information on Result #700488
Linear OA(240, 51, F2, 18) (dual of [51, 11, 19]-code), using construction XX applied to C1 = C({1,3,5,7,15}), C2 = C([1,11]), C3 = C1 + C2 = C([1,7]), and C∩ = C1 ∩ C2 = C([1,15]) based on
- linear OA(225, 31, F2, 14) (dual of [31, 6, 15]-code), using the primitive cyclic code C(A) with length 31 = 25−1, defining set A = {1,3,5,7,15}, and minimum distance d ≥ |{5,10,15,…,8}|+1 = 15 (BCH-bound) [i]
- linear OA(225, 31, F2, 14) (dual of [31, 6, 15]-code), using the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(230, 31, F2, 30) (dual of [31, 1, 31]-code or 31-arc in PG(29,2)), using the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(220, 31, F2, 10) (dual of [31, 11, 11]-code), using the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(25, 10, F2, 3) (dual of [10, 5, 4]-code or 10-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(25, 10, F2, 3) (dual of [10, 5, 4]-code or 10-cap in PG(4,2)) (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(241, 52, F2, 19) (dual of [52, 11, 20]-code) | [i] | Adding a Parity Check Bit | |
| 2 | Linear OOA(240, 17, F2, 3, 18) (dual of [(17, 3), 11, 19]-NRT-code) | [i] | OOA Folding | |