Information on Result #1060220
Linear OOA(3187, 2097699, F3, 4, 16) (dual of [(2097699, 4), 8390609, 17]-NRT-code), using OOA 2-folding based on linear OOA(3187, 4195398, F3, 2, 16) (dual of [(4195398, 2), 8390609, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(336, 1097, F3, 2, 8) (dual of [(1097, 2), 2158, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(336, 2194, F3, 8) (dual of [2194, 2158, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(336, 2187, F3, 8) (dual of [2187, 2151, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(329, 2187, F3, 7) (dual of [2187, 2158, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(30, 7, F3, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- OOA 2-folding [i] based on linear OA(336, 2194, F3, 8) (dual of [2194, 2158, 9]-code), using
- linear OOA(3151, 4194301, F3, 2, 16) (dual of [(4194301, 2), 8388451, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3151, 8388602, F3, 16) (dual of [8388602, 8388451, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- OOA 2-folding [i] based on linear OA(3151, 8388602, F3, 16) (dual of [8388602, 8388451, 17]-code), using
- linear OOA(336, 1097, F3, 2, 8) (dual of [(1097, 2), 2158, 9]-NRT-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(3188, 2097699, F3, 4, 16) (dual of [(2097699, 4), 8390608, 17]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3189, 2097699, F3, 4, 16) (dual of [(2097699, 4), 8390607, 17]-NRT-code) | [i] | ||