Information on Result #700960
Linear OA(49, 18, F4, 7) (dual of [18, 9, 8]-code), using construction X applied to C({0,1,3}) ⊂ C({1,3}) 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
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(413, 35, F4, 7) (dual of [35, 22, 8]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(236, 54, F2, 15) (dual of [54, 18, 16]-code) | [i] | Concatenation of Two Codes | |
| 3 | Linear OOA(290, 54, F2, 2, 39) (dual of [(54, 2), 18, 40]-NRT-code) | [i] | Concatenation of Two NRT-Codes | |
| 4 | Linear OA(446, 82, F4, 21) (dual of [82, 36, 22]-code) | [i] | Construction XX with Cyclic Codes | |
| 5 | Linear OA(449, 84, F4, 22) (dual of [84, 35, 23]-code) | [i] | ||
| 6 | Linear OA(453, 88, F4, 23) (dual of [88, 35, 24]-code) | [i] | ||
| 7 | Linear OA(4152, 277, F4, 54) (dual of [277, 125, 55]-code) | [i] | ||
| 8 | Linear OA(4256, 1048, F4, 70) (dual of [1048, 792, 71]-code) | [i] | ||
| 9 | Linear OA(4255, 1046, F4, 70) (dual of [1046, 791, 71]-code) | [i] | ||
| 10 | Linear OA(4260, 1046, F4, 71) (dual of [1046, 786, 72]-code) | [i] | ||
| 11 | Linear OA(465, 82, F4, 35) (dual of [82, 17, 36]-code) | [i] | ||
| 12 | Linear OOA(49, 9, F4, 2, 7) (dual of [(9, 2), 9, 8]-NRT-code) | [i] | OOA Folding | |
| 13 | Linear OOA(49, 6, F4, 3, 7) (dual of [(6, 3), 9, 8]-NRT-code) | [i] | ||