Information on Result #1202654
Digital (57, 74, 1048624)-net over F81, using net defined by OOA based on linear OOA(8174, 1048624, F81, 20, 17) (dual of [(1048624, 20), 20972406, 18]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(8174, 2097249, F81, 4, 17) (dual of [(2097249, 4), 8388922, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8174, 2097250, F81, 4, 17) (dual of [(2097250, 4), 8388926, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(819, 100, F81, 4, 8) (dual of [(100, 4), 391, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(4;F,391P) [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- linear OOA(8165, 2097150, F81, 4, 17) (dual of [(2097150, 4), 8388535, 18]-NRT-code), using
- OOA 4-folding [i] based on linear OA(8165, 8388600, F81, 17) (dual of [8388600, 8388535, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(8165, large, F81, 17) (dual of [large, large−65, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8165, large, F81, 17) (dual of [large, large−65, 18]-code), using
- OOA 4-folding [i] based on linear OA(8165, 8388600, F81, 17) (dual of [8388600, 8388535, 18]-code), using
- linear OOA(819, 100, F81, 4, 8) (dual of [(100, 4), 391, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(8174, 2097250, F81, 4, 17) (dual of [(2097250, 4), 8388926, 18]-NRT-code), using
Mode: Constructive and 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
The following results depend on this result:
Result | This result only | Method | ||
---|---|---|---|---|
1 | Digital (131, 148, 2097248)-net over F9 | [i] | Trace Code for Nets |