Information on Result #1621115
Linear OOA(3205, 1922883, F3, 5, 19) (dual of [(1922883, 5), 9614210, 20]-NRT-code), using OOA 2-folding based on linear OOA(3205, 3845766, F3, 3, 19) (dual of [(3845766, 3), 11537093, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3205, 3845767, F3, 3, 19) (dual of [(3845767, 3), 11537096, 20]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3205, 3845767, F3, 2, 19) (dual of [(3845767, 2), 7691329, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3205, 4194357, F3, 2, 19) (dual of [(4194357, 2), 8388509, 20]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(324, 56, F3, 2, 9) (dual of [(56, 2), 88, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (15, 24, 56)-net over F3, using
- trace code for nets [i] based on digital (3, 12, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- trace code for nets [i] based on digital (3, 12, 28)-net over F9, using
- extracting embedded OOA [i] based on digital (15, 24, 56)-net over F3, 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(324, 56, F3, 2, 9) (dual of [(56, 2), 88, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(3205, 4194357, F3, 2, 19) (dual of [(4194357, 2), 8388509, 20]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3205, 3845767, F3, 2, 19) (dual of [(3845767, 2), 7691329, 20]-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.