Information on Result #613544
Linear OA(57, 25, F5, 4) (dual of [25, 18, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4
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(5147, 654, F5, 42) (dual of [654, 507, 43]-code) | [i] | Construction XX with a Chain of Cyclic Codes | |
| 2 | Linear OA(5139, 654, F5, 40) (dual of [654, 515, 41]-code) | [i] | ||
| 3 | Linear OA(5115, 654, F5, 32) (dual of [654, 539, 33]-code) | [i] | ||
| 4 | Linear OA(5107, 654, F5, 30) (dual of [654, 547, 31]-code) | [i] | ||
| 5 | Linear OA(583, 654, F5, 22) (dual of [654, 571, 23]-code) | [i] | ||
| 6 | Linear OA(575, 654, F5, 20) (dual of [654, 579, 21]-code) | [i] | ||
| 7 | Linear OA(510, 28, F5, 6) (dual of [28, 18, 7]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 8 | Linear OA(57, 27, F5, 4) (dual of [27, 20, 5]-code) | [i] | ✔ | |
| 9 | Linear OA(512, 30, F5, 7) (dual of [30, 18, 8]-code) | [i] | ✔ | |
| 10 | Linear OA(5137, 653, F5, 41) (dual of [653, 516, 42]-code) | [i] | Construction XX with a Chain of Extended Narrow-Sense BCH Codes | |
| 11 | Linear OA(5121, 653, F5, 36) (dual of [653, 532, 37]-code) | [i] | ||
| 12 | Linear OA(591, 653, F5, 26) (dual of [653, 562, 27]-code) | [i] | ||
| 13 | Linear OA(575, 653, F5, 21) (dual of [653, 578, 22]-code) | [i] | ||
| 14 | Linear OA(559, 653, F5, 16) (dual of [653, 594, 17]-code) | [i] | ||
| 15 | Linear OA(515, 32, F5, 8) (dual of [32, 17, 9]-code) | [i] | ✔ | |
| 16 | Linear OA(513, 32, F5, 7) (dual of [32, 19, 8]-code) | [i] | ✔ | |