Information on Result #682875
Linear OA(592, 3137, F5, 23) (dual of [3137, 3045, 24]-code), using construction X applied to C([0,11]) ⊂ C([0,10]) based on
- linear OA(591, 3126, F5, 23) (dual of [3126, 3035, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 3126 | 510−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(581, 3126, F5, 21) (dual of [3126, 3045, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 3126 | 510−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(51, 11, F5, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(593, 3138, F5, 23) (dual of [3138, 3045, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(594, 3139, F5, 23) (dual of [3139, 3045, 24]-code) | [i] | ||
| 3 | Linear OOA(592, 2305, F5, 2, 23) (dual of [(2305, 2), 4518, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(592, 2305, F5, 3, 23) (dual of [(2305, 3), 6823, 24]-NRT-code) | [i] | ||
| 5 | Digital (69, 92, 2305)-net over F5 | [i] | ||
| 6 | Linear OA(594, 3141, F5, 23) (dual of [3141, 3047, 24]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OA(595, 3146, F5, 23) (dual of [3146, 3051, 24]-code) | [i] | ||
| 8 | Linear OA(596, 3157, F5, 23) (dual of [3157, 3061, 24]-code) | [i] | ||
| 9 | Linear OA(597, 3181, F5, 23) (dual of [3181, 3084, 24]-code) | [i] | ||
| 10 | Linear OA(598, 3231, F5, 23) (dual of [3231, 3133, 24]-code) | [i] | ||
| 11 | Linear OA(599, 3325, F5, 23) (dual of [3325, 3226, 24]-code) | [i] | ||
| 12 | Linear OA(5100, 3480, F5, 23) (dual of [3480, 3380, 24]-code) | [i] | ||
| 13 | Linear OA(594, 3140, F5, 23) (dual of [3140, 3046, 24]-code) | [i] | Construction X with Varšamov Bound | |
| 14 | Linear OOA(592, 1568, F5, 2, 23) (dual of [(1568, 2), 3044, 24]-NRT-code) | [i] | OOA Folding | |
| 15 | Linear OOA(592, 1045, F5, 3, 23) (dual of [(1045, 3), 3043, 24]-NRT-code) | [i] | ||