Information on Result #682954
Linear OA(5142, 3131, F5, 36) (dual of [3131, 2989, 37]-code), using construction X applied to Ce(35) ⊂ Ce(33) based on
- linear OA(5141, 3125, F5, 36) (dual of [3125, 2984, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(5136, 3125, F5, 34) (dual of [3125, 2989, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(51, 6, F5, 1) (dual of [6, 5, 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(5141, 3130, F5, 35) (dual of [3130, 2989, 36]-code) | [i] | Truncation | |
| 2 | Linear OOA(5142, 2656, F5, 2, 36) (dual of [(2656, 2), 5170, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(5142, 2656, F5, 3, 36) (dual of [(2656, 3), 7826, 37]-NRT-code) | [i] | ||
| 4 | Digital (106, 142, 2656)-net over F5 | [i] | ||
| 5 | Linear OA(5146, 3158, F5, 36) (dual of [3158, 3012, 37]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(5147, 3189, F5, 36) (dual of [3189, 3042, 37]-code) | [i] | ||
| 7 | Linear OA(5148, 3248, F5, 36) (dual of [3248, 3100, 37]-code) | [i] | ||
| 8 | Linear OA(5149, 3343, F5, 36) (dual of [3343, 3194, 37]-code) | [i] | ||
| 9 | Linear OOA(5142, 1565, F5, 2, 36) (dual of [(1565, 2), 2988, 37]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(5142, 1043, F5, 3, 36) (dual of [(1043, 3), 2987, 37]-NRT-code) | [i] | ||