Information on Result #1715456
Digital (198, 223, 144123)-net over F3, using net defined by OOA based on linear OOA(3223, 144123, F3, 28, 25) (dual of [(144123, 28), 4035221, 26]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(3223, 432370, F3, 4, 25) (dual of [(432370, 4), 1729257, 26]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3223, 432370, F3, 3, 25) (dual of [(432370, 3), 1296887, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3223, 531463, F3, 3, 25) (dual of [(531463, 3), 1594166, 26]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3222, 531463, F3, 3, 25) (dual of [(531463, 3), 1594167, 26]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3222, 1594389, F3, 25) (dual of [1594389, 1594167, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(3209, 1594324, F3, 25) (dual of [1594324, 1594115, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(3157, 1594324, F3, 19) (dual of [1594324, 1594167, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(313, 65, F3, 5) (dual of [65, 52, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(313, 80, F3, 5) (dual of [80, 67, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(313, 80, F3, 5) (dual of [80, 67, 6]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- OOA 3-folding [i] based on linear OA(3222, 1594389, F3, 25) (dual of [1594389, 1594167, 26]-code), using
- 31 times duplication [i] based on linear OOA(3222, 531463, F3, 3, 25) (dual of [(531463, 3), 1594167, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3223, 531463, F3, 3, 25) (dual of [(531463, 3), 1594166, 26]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3223, 432370, F3, 3, 25) (dual of [(432370, 3), 1296887, 26]-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, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.