Information on Result #904505
Linear OOA(8180, 4197664, F81, 2, 16) (dual of [(4197664, 2), 8395248, 17]-NRT-code), using (u, u+v)-construction based on
- linear OOA(8119, 3363, F81, 2, 8) (dual of [(3363, 2), 6707, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(814, 82, F81, 2, 4) (dual of [(82, 2), 160, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;160,81) [i]
- linear OOA(8115, 3281, F81, 2, 8) (dual of [(3281, 2), 6547, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8115, 6562, F81, 8) (dual of [6562, 6547, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(8115, 6563, F81, 8) (dual of [6563, 6548, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] 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]
- linear OA(8113, 6561, F81, 7) (dual of [6561, 6548, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(8115, 6563, F81, 8) (dual of [6563, 6548, 9]-code), using
- OOA 2-folding [i] based on linear OA(8115, 6562, F81, 8) (dual of [6562, 6547, 9]-code), using
- linear OOA(814, 82, F81, 2, 4) (dual of [(82, 2), 160, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(8161, 4194301, F81, 2, 16) (dual of [(4194301, 2), 8388541, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8161, 8388602, F81, 16) (dual of [8388602, 8388541, 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 2-folding [i] based on linear OA(8161, 8388602, F81, 16) (dual of [8388602, 8388541, 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, 2098832, F81, 4, 16) (dual of [(2098832, 4), 8395248, 17]-NRT-code) | [i] | OOA Folding | |