Information on Result #686805
Linear OA(8159, 32786, F8, 36) (dual of [32786, 32627, 37]-code), using construction X applied to Ce(35) ⊂ Ce(32) based on
- linear OA(8156, 32768, F8, 36) (dual of [32768, 32612, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(8141, 32768, F8, 33) (dual of [32768, 32627, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(83, 18, F8, 2) (dual of [18, 15, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-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(8160, 32787, F8, 36) (dual of [32787, 32627, 37]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8159, 30394, F8, 2, 36) (dual of [(30394, 2), 60629, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8159, 30394, F8, 3, 36) (dual of [(30394, 3), 91023, 37]-NRT-code) | [i] | ||
| 4 | Digital (123, 159, 30394)-net over F8 | [i] | ||
| 5 | Linear OOA(8159, 16393, F8, 2, 36) (dual of [(16393, 2), 32627, 37]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8159, 10928, F8, 3, 36) (dual of [(10928, 3), 32625, 37]-NRT-code) | [i] | ||