Information on Result #1301684
Linear OA(5109, 137, F5, 64) (dual of [137, 28, 65]-code), using construction X with Varšamov bound based on
- linear OA(5103, 130, F5, 64) (dual of [130, 27, 65]-code), using
- construction X applied to Ce(63) ⊂ Ce(61) [i] based on
- linear OA(5102, 125, F5, 64) (dual of [125, 23, 65]-code), using an extension Ce(63) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,63], and designed minimum distance d ≥ |I|+1 = 64 [i]
- linear OA(598, 125, F5, 62) (dual of [125, 27, 63]-code), using an extension Ce(61) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,61], and designed minimum distance d ≥ |I|+1 = 62 [i]
- linear OA(51, 5, F5, 1) (dual of [5, 4, 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
- construction X applied to Ce(63) ⊂ Ce(61) [i] based on
- linear OA(5103, 131, F5, 58) (dual of [131, 28, 59]-code), using Gilbert–Varšamov bound and bm = 5103 > Vbs−1(k−1) = 916653 790838 264584 056935 513636 262037 817975 507876 741954 444632 075044 851225 [i]
- linear OA(55, 6, F5, 5) (dual of [6, 1, 6]-code or 6-arc in PG(4,5)), using
- dual of repetition code with length 6 [i]
Mode: 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(5110, 138, F5, 64) (dual of [138, 28, 65]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(5108, 136, F5, 63) (dual of [136, 28, 64]-code) | [i] | Truncation | |