Information on Result #1758801
Digital (226, 244, 2045875)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2244, 2045875, F2, 4, 18) (dual of [(2045875, 4), 8183256, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2244, 2097278, F2, 4, 18) (dual of [(2097278, 4), 8388868, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2244, 4194556, F2, 2, 18) (dual of [(4194556, 2), 8388868, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2244, 4194557, F2, 2, 18) (dual of [(4194557, 2), 8388870, 19]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(237, 256, F2, 2, 9) (dual of [(256, 2), 475, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(237, 512, F2, 9) (dual of [512, 475, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- OOA 2-folding [i] based on linear OA(237, 512, F2, 9) (dual of [512, 475, 10]-code), using
- linear OOA(2207, 4194301, F2, 2, 18) (dual of [(4194301, 2), 8388395, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2207, 8388602, F2, 18) (dual of [8388602, 8388395, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
- OOA 2-folding [i] based on linear OA(2207, 8388602, F2, 18) (dual of [8388602, 8388395, 19]-code), using
- linear OOA(237, 256, F2, 2, 9) (dual of [(256, 2), 475, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(2244, 4194557, F2, 2, 18) (dual of [(4194557, 2), 8388870, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2244, 4194556, F2, 2, 18) (dual of [(4194556, 2), 8388868, 19]-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.