Information on Result #686382
Linear OA(8150, 2097169, F8, 24) (dual of [2097169, 2097019, 25]-code), using construction XX applied to Ce(24) ⊂ Ce(21) ⊂ Ce(20) based on
- 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(8134, 2097152, F8, 22) (dual of [2097152, 2097018, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(8127, 2097152, F8, 21) (dual of [2097152, 2097025, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(8150, 1690962, F8, 2, 24) (dual of [(1690962, 2), 3381774, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8150, 1690962, F8, 3, 24) (dual of [(1690962, 3), 5072736, 25]-NRT-code) | [i] | ||
| 3 | Digital (126, 150, 1690962)-net over F8 | [i] | ||
| 4 | Linear OOA(8150, 1048584, F8, 2, 24) (dual of [(1048584, 2), 2097018, 25]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8150, 699056, F8, 3, 24) (dual of [(699056, 3), 2097018, 25]-NRT-code) | [i] | ||
| 6 | Linear OOA(8150, 174764, F8, 24, 24) (dual of [(174764, 24), 4194186, 25]-NRT-code) | [i] | OA Folding and Stacking | |