Information on Result #613589
Linear OA(59, 14, F5, 7) (dual of [14, 5, 8]-code), using construction X applied to C([0,3]) ⊂ C([1,3]) based on
- linear OA(59, 13, F5, 7) (dual of [13, 4, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 13 | 54−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(58, 13, F5, 6) (dual of [13, 5, 7]-code), using the narrow-sense BCH-code C(I) with length 13 | 54−1, defining interval I = [1,3], and minimum distance d ≥ |{−5,−3,−1,…,5}|+1 = 7 (BCH-bound) [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 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(557, 638, F5, 15) (dual of [638, 581, 16]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(569, 3138, F5, 15) (dual of [3138, 3069, 16]-code) | [i] | ||
| 3 | Linear OA(581, 15638, F5, 15) (dual of [15638, 15557, 16]-code) | [i] | ||
| 4 | Linear OA(593, 78138, F5, 15) (dual of [78138, 78045, 16]-code) | [i] | ||
| 5 | Linear OA(5105, 390638, F5, 15) (dual of [390638, 390533, 16]-code) | [i] | ||
| 6 | Linear OA(5117, 1953138, F5, 15) (dual of [1953138, 1953021, 16]-code) | [i] | ||
| 7 | Linear OA(565, 3139, F5, 14) (dual of [3139, 3074, 15]-code) | [i] | ||
| 8 | Linear OA(576, 15639, F5, 14) (dual of [15639, 15563, 15]-code) | [i] | ||
| 9 | Linear OA(587, 78139, F5, 14) (dual of [78139, 78052, 15]-code) | [i] | ||
| 10 | Linear OA(598, 390639, F5, 14) (dual of [390639, 390541, 15]-code) | [i] | ||
| 11 | Linear OA(5109, 1953139, F5, 14) (dual of [1953139, 1953030, 15]-code) | [i] | ||
| 12 | Linear OA(5120, 140, F5, 73) (dual of [140, 20, 74]-code) | [i] | Construction X with Cyclic Codes | |
| 13 | Linear OA(5107, 139, F5, 56) (dual of [139, 32, 57]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 14 | Linear OA(570, 139, F5, 31) (dual of [139, 69, 32]-code) | [i] | ||
| 15 | Linear OA(572, 140, F5, 32) (dual of [140, 68, 33]-code) | [i] | Construction XX with a Chain of Extended Narrow-Sense BCH Codes | |