Information on Result #1670578
Linear OOA(2237, 6290, F2, 6, 31) (dual of [(6290, 6), 37503, 32]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2237, 6290, F2, 5, 31) (dual of [(6290, 5), 31213, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2237, 6561, F2, 5, 31) (dual of [(6561, 5), 32568, 32]-NRT-code), using
- 24 times duplication [i] based on linear OOA(2233, 6561, F2, 5, 31) (dual of [(6561, 5), 32572, 32]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2233, 32805, F2, 31) (dual of [32805, 32572, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- linear OA(2226, 32768, F2, 31) (dual of [32768, 32542, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2196, 32768, F2, 27) (dual of [32768, 32572, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(30) ⊂ Ce(26) [i] based on
- OOA 5-folding [i] based on linear OA(2233, 32805, F2, 31) (dual of [32805, 32572, 32]-code), using
- 24 times duplication [i] based on linear OOA(2233, 6561, F2, 5, 31) (dual of [(6561, 5), 32572, 32]-NRT-code), using
Mode: 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.