Information on Result #686376
Linear OA(8171, 2097169, F8, 28) (dual of [2097169, 2096998, 29]-code), using construction XX applied to Ce(27) ⊂ Ce(25) ⊂ Ce(24) based on
- linear OA(8169, 2097152, F8, 28) (dual of [2097152, 2096983, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(8155, 2097152, F8, 26) (dual of [2097152, 2096997, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(8148, 2097152, F8, 25) (dual of [2097152, 2097004, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(81, 16, F8, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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 OOA(8171, 1210622, F8, 2, 28) (dual of [(1210622, 2), 2421073, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8171, 1210622, F8, 3, 28) (dual of [(1210622, 3), 3631695, 29]-NRT-code) | [i] | ||
| 3 | Digital (143, 171, 1210622)-net over F8 | [i] | ||
| 4 | Linear OOA(8171, 1048584, F8, 2, 28) (dual of [(1048584, 2), 2096997, 29]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8171, 699056, F8, 3, 28) (dual of [(699056, 3), 2096997, 29]-NRT-code) | [i] | ||