Information on Result #1193502
Digital (100, 111, 3991944)-net over F9, using net defined by OOA based on linear OOA(9111, 3991944, F9, 15, 11) (dual of [(3991944, 15), 59879049, 12]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(9111, 7983889, F9, 3, 11) (dual of [(7983889, 3), 23951556, 12]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(929, 2391487, F9, 3, 5) (dual of [(2391487, 3), 7174432, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(929, 4782975, F9, 5) (dual of [4782975, 4782946, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(929, 4782976, F9, 5) (dual of [4782976, 4782947, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(929, 4782969, F9, 5) (dual of [4782969, 4782940, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(922, 4782969, F9, 4) (dual of [4782969, 4782947, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(90, 7, F9, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- discarding factors / shortening the dual code based on linear OA(929, 4782976, F9, 5) (dual of [4782976, 4782947, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(929, 4782975, F9, 5) (dual of [4782975, 4782946, 6]-code), using
- linear OOA(982, 5592402, F9, 3, 11) (dual of [(5592402, 3), 16777124, 12]-NRT-code), using
- trace code [i] based on linear OOA(8141, 2796201, F81, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8141, large, F81, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(8141, large, F81, 11) (dual of [large, large−41, 12]-code), using
- trace code [i] based on linear OOA(8141, 2796201, F81, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
- linear OOA(929, 2391487, F9, 3, 5) (dual of [(2391487, 3), 7174432, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
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
None.