Information on Result #682958
Linear OA(5126, 3130, F5, 32) (dual of [3130, 3004, 33]-code), using construction X applied to Ce(31) ⊂ Ce(30) based on
- linear OA(5126, 3125, F5, 32) (dual of [3125, 2999, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(5121, 3125, F5, 31) (dual of [3125, 3004, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(50, 5, F5, 0) (dual of [5, 5, 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(5127, 3131, F5, 32) (dual of [3131, 3004, 33]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(5131, 3156, F5, 32) (dual of [3156, 3025, 33]-code) | [i] | Varšamov–Edel Lengthening | |
| 3 | Linear OA(5132, 3185, F5, 32) (dual of [3185, 3053, 33]-code) | [i] | ||
| 4 | Linear OA(5133, 3240, F5, 32) (dual of [3240, 3107, 33]-code) | [i] | ||
| 5 | Linear OA(5134, 3335, F5, 32) (dual of [3335, 3201, 33]-code) | [i] | ||
| 6 | Linear OA(5135, 3472, F5, 32) (dual of [3472, 3337, 33]-code) | [i] | ||
| 7 | Linear OA(5136, 3640, F5, 32) (dual of [3640, 3504, 33]-code) | [i] | ||
| 8 | Linear OA(5137, 3828, F5, 32) (dual of [3828, 3691, 33]-code) | [i] | ||
| 9 | Linear OOA(5126, 1565, F5, 2, 32) (dual of [(1565, 2), 3004, 33]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(5126, 1043, F5, 3, 32) (dual of [(1043, 3), 3003, 33]-NRT-code) | [i] | ||