Information on Result #686887
Linear OA(8172, 32809, F8, 37) (dual of [32809, 32637, 38]-code), using construction X applied to Ce(36) ⊂ Ce(29) based on
- linear OA(8161, 32768, F8, 37) (dual of [32768, 32607, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(8131, 32768, F8, 30) (dual of [32768, 32637, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(811, 41, F8, 6) (dual of [41, 30, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(811, 63, F8, 6) (dual of [63, 52, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(811, 63, F8, 6) (dual of [63, 52, 7]-code), 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(8173, 32810, F8, 37) (dual of [32810, 32637, 38]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8172, 16404, F8, 2, 37) (dual of [(16404, 2), 32636, 38]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8172, 10936, F8, 3, 37) (dual of [(10936, 3), 32636, 38]-NRT-code) | [i] | ||