Information on Result #731708
Linear OA(236, 54, F2, 15) (dual of [54, 18, 16]-code), using concatenation of two codes based on
- linear OA(49, 18, F4, 7) (dual of [18, 9, 8]-code), using
- construction X applied to C({0,1,3}) ⊂ C({1,3}) [i] based on
- linear OA(49, 17, F4, 7) (dual of [17, 8, 8]-code), using the cyclic code C(A) with length 17 | 44−1, defining set A = {0,1,3}, and minimum distance d ≥ |{1,5}| + |{−6,−5,…,0}∖{−3}| = 8 (general Roos-bound) [i]
- linear OA(48, 17, F4, 6) (dual of [17, 9, 7]-code), using the cyclic code C(A) with length 17 | 44−1, defining set A = {1,3}, and minimum distance d ≥ |{−5,−3,−1,…,5}|+1 = 7 (BCH-bound) [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to C({0,1,3}) ⊂ C({1,3}) [i] based on
- linear OA(21, 3, F2, 1) (dual of [3, 2, 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
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(235, 53, F2, 14) (dual of [53, 18, 15]-code) | [i] | Truncation | |
| 2 | Linear OA(2156, 175, F2, 63) (dual of [175, 19, 64]-code) | [i] | Construction X with De Boer–Brouwer Codes | |
| 3 | Linear OOA(236, 27, F2, 2, 15) (dual of [(27, 2), 18, 16]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(236, 18, F2, 3, 15) (dual of [(18, 3), 18, 16]-NRT-code) | [i] | ||