Information on Result #1082621
Linear OOA(8180, 2098872, F81, 4, 16) (dual of [(2098872, 4), 8395408, 17]-NRT-code), using (u, u+v)-construction based on
- linear OOA(8119, 1722, F81, 4, 8) (dual of [(1722, 4), 6869, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(814, 82, F81, 4, 4) (dual of [(82, 4), 324, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(4;324,81) [i]
- linear OOA(8115, 1640, F81, 4, 8) (dual of [(1640, 4), 6545, 9]-NRT-code), using
- OOA 4-folding [i] based on linear OA(8115, 6560, F81, 8) (dual of [6560, 6545, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(8115, 6561, F81, 8) (dual of [6561, 6546, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(8115, 6561, F81, 8) (dual of [6561, 6546, 9]-code), using
- OOA 4-folding [i] based on linear OA(8115, 6560, F81, 8) (dual of [6560, 6545, 9]-code), using
- linear OOA(814, 82, F81, 4, 4) (dual of [(82, 4), 324, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(8161, 2097150, F81, 4, 16) (dual of [(2097150, 4), 8388539, 17]-NRT-code), using
- OOA 4-folding [i] based on linear OA(8161, 8388600, F81, 16) (dual of [8388600, 8388539, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(8161, large, F81, 16) (dual of [large, large−61, 17]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(8161, large, F81, 16) (dual of [large, large−61, 17]-code), using
- OOA 4-folding [i] based on linear OA(8161, 8388600, F81, 16) (dual of [8388600, 8388539, 17]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(8180, 1049435, F81, 20, 16) (dual of [(1049435, 20), 20988620, 17]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |