Information on Result #1716274
Digital (140, 171, 1209)-net over F3, using net defined by OOA based on linear OOA(3171, 1209, F3, 35, 31) (dual of [(1209, 35), 42144, 32]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(3171, 3628, F3, 5, 31) (dual of [(3628, 5), 17969, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3171, 3629, F3, 5, 31) (dual of [(3629, 5), 17974, 32]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3171, 3629, F3, 31) (dual of [3629, 3458, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(3171, 6598, F3, 31) (dual of [6598, 6427, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,12]) [i] based on
- linear OA(3161, 6562, F3, 31) (dual of [6562, 6401, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(3129, 6562, F3, 25) (dual of [6562, 6433, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(310, 36, F3, 5) (dual of [36, 26, 6]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- linear OA(31, 12, F3, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(33, 12, F3, 2) (dual of [12, 9, 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(36, 12, F3, 5) (dual of [12, 6, 6]-code), using
- extended Golay code Ge(3) [i]
- linear OA(31, 12, F3, 1) (dual of [12, 11, 2]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- construction X applied to C([0,15]) ⊂ C([0,12]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3171, 6598, F3, 31) (dual of [6598, 6427, 32]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3171, 3629, F3, 31) (dual of [3629, 3458, 32]-code), using
- discarding factors / shortening the dual code based on linear OOA(3171, 3629, F3, 5, 31) (dual of [(3629, 5), 17974, 32]-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.