Information on Result #1778915
Digital (165, 187, 1924217)-net over F4, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4187, 1924217, F4, 2, 22) (dual of [(1924217, 2), 3848247, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4187, 2097179, F4, 2, 22) (dual of [(2097179, 2), 4194171, 23]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4185, 2097178, F4, 2, 22) (dual of [(2097178, 2), 4194171, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4185, 4194356, F4, 22) (dual of [4194356, 4194171, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(4177, 4194304, F4, 22) (dual of [4194304, 4194127, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(4133, 4194304, F4, 17) (dual of [4194304, 4194171, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(48, 52, F4, 4) (dual of [52, 44, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(48, 85, F4, 4) (dual of [85, 77, 5]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- OOA 2-folding [i] based on linear OA(4185, 4194356, F4, 22) (dual of [4194356, 4194171, 23]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4185, 2097178, F4, 2, 22) (dual of [(2097178, 2), 4194171, 23]-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.