Information on Result #737969
Linear OA(1694, 1048629, F16, 18) (dual of [1048629, 1048535, 19]-code), using construction X applied to Ce(17) ⊂ Ce(8) based on
- linear OA(1681, 1048576, F16, 18) (dual of [1048576, 1048495, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(1641, 1048576, F16, 9) (dual of [1048576, 1048535, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(1613, 53, F16, 8) (dual of [53, 40, 9]-code), using
- construction X applied to C([13,20]) ⊂ C([14,20]) [i] based on
- linear OA(1613, 51, F16, 8) (dual of [51, 38, 9]-code), using the BCH-code C(I) with length 51 | 162−1, defining interval I = {13,14,…,20}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(1611, 51, F16, 7) (dual of [51, 40, 8]-code), using the BCH-code C(I) with length 51 | 162−1, defining interval I = {14,15,…,20}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(160, 2, F16, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to C([13,20]) ⊂ C([14,20]) [i] based on
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(1694, 524314, F16, 2, 18) (dual of [(524314, 2), 1048534, 19]-NRT-code) | [i] | OOA Folding | |