Information on Result #1606451
Linear OOA(3171, 4194346, F3, 4, 16) (dual of [(4194346, 4), 16777213, 17]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3171, 4194346, F3, 2, 16) (dual of [(4194346, 2), 8388521, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(320, 45, F3, 2, 8) (dual of [(45, 2), 70, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(320, 45, F3, 8) (dual of [45, 25, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(320, 46, F3, 8) (dual of [46, 26, 9]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- linear OA(33, 11, F3, 2) (dual of [11, 8, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- linear OA(35, 11, F3, 4) (dual of [11, 6, 5]-code), using
- Golay code G(3) [i]
- linear OA(312, 24, F3, 8) (dual of [24, 12, 9]-code), using
- extended quadratic residue code Qe(24,3) [i]
- linear OA(33, 11, F3, 2) (dual of [11, 8, 3]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(320, 46, F3, 8) (dual of [46, 26, 9]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(320, 45, F3, 8) (dual of [45, 25, 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(320, 45, F3, 2, 8) (dual of [(45, 2), 70, 9]-NRT-code), using
Mode: 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(3171, 2097172, F3, 20, 16) (dual of [(2097172, 20), 41943269, 17]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |