Information on Result #1609547
Linear OOA(3211, 4194456, F3, 4, 19) (dual of [(4194456, 4), 16777613, 20]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3211, 4194456, F3, 2, 19) (dual of [(4194456, 2), 8388701, 20]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(330, 155, F3, 2, 9) (dual of [(155, 2), 280, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(330, 155, F3, 9) (dual of [155, 125, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(330, 242, F3, 9) (dual of [242, 212, 10]-code), using
- the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding factors / shortening the dual code based on linear OA(330, 242, F3, 9) (dual of [242, 212, 10]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(330, 155, F3, 9) (dual of [155, 125, 10]-code), using
- linear OOA(3181, 4194301, F3, 2, 19) (dual of [(4194301, 2), 8388421, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3181, 8388602, F3, 19) (dual of [8388602, 8388421, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- OOA 2-folding [i] based on linear OA(3181, 8388602, F3, 19) (dual of [8388602, 8388421, 20]-code), using
- linear OOA(330, 155, F3, 2, 9) (dual of [(155, 2), 280, 10]-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
None.