Information on Result #2258835
Linear OA(2175, 32807, F2, 22) (dual of [32807, 32632, 23]-code), using 3 times code embedding in larger space based on linear OA(2172, 32804, F2, 22) (dual of [32804, 32632, 23]-code), using
- 1 times truncation [i] based on linear OA(2173, 32805, F2, 23) (dual of [32805, 32632, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(2166, 32768, F2, 23) (dual of [32768, 32602, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2136, 32768, F2, 19) (dual of [32768, 32632, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(27, 37, F2, 3) (dual of [37, 30, 4]-code or 37-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
None.