Information on Result #683013
Linear OA(537, 3137, F5, 9) (dual of [3137, 3100, 10]-code), using construction X4 applied to Ce(8) ⊂ Ce(6) based on
- linear OA(536, 3125, F5, 9) (dual of [3125, 3089, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(526, 3125, F5, 7) (dual of [3125, 3099, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(511, 12, F5, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,5)), using
- dual of repetition code with length 12 [i]
- linear OA(51, 12, F5, 1) (dual of [12, 11, 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(538, 3138, F5, 9) (dual of [3138, 3100, 10]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(537, 3137, F5, 2, 9) (dual of [(3137, 2), 6237, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(537, 3137, F5, 3, 9) (dual of [(3137, 3), 9374, 10]-NRT-code) | [i] | ||
| 4 | Digital (28, 37, 3137)-net over F5 | [i] | ||
| 5 | Linear OA(538, 3145, F5, 9) (dual of [3145, 3107, 10]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(539, 3181, F5, 9) (dual of [3181, 3142, 10]-code) | [i] | ||
| 7 | Linear OA(540, 3327, F5, 9) (dual of [3327, 3287, 10]-code) | [i] | ||
| 8 | Linear OA(541, 3731, F5, 9) (dual of [3731, 3690, 10]-code) | [i] | ||
| 9 | Linear OA(542, 4437, F5, 9) (dual of [4437, 4395, 10]-code) | [i] | ||
| 10 | Linear OA(538, 3139, F5, 9) (dual of [3139, 3101, 10]-code) | [i] | Construction X with Varšamov Bound | |
| 11 | Linear OOA(537, 784, F5, 9, 9) (dual of [(784, 9), 7019, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |