Information on Result #2788821
Linear OOA(2259, 2098178, F2, 4, 19) (dual of [(2098178, 4), 8392453, 20]-NRT-code), using 21 times duplication based on linear OOA(2258, 2098178, F2, 4, 19) (dual of [(2098178, 4), 8392454, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2258, 4196356, F2, 2, 19) (dual of [(4196356, 2), 8392454, 20]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(250, 2055, F2, 2, 9) (dual of [(2055, 2), 4060, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(250, 4110, F2, 9) (dual of [4110, 4060, 10]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(249, 4096, F2, 9) (dual of [4096, 4047, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(237, 4096, F2, 7) (dual of [4096, 4059, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(213, 14, F2, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,2)), using
- dual of repetition code with length 14 [i]
- linear OA(21, 14, F2, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- OOA 2-folding [i] based on linear OA(250, 4110, F2, 9) (dual of [4110, 4060, 10]-code), using
- linear OOA(2208, 4194301, F2, 2, 19) (dual of [(4194301, 2), 8388394, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2208, 8388602, F2, 19) (dual of [8388602, 8388394, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- OOA 2-folding [i] based on linear OA(2208, 8388602, F2, 19) (dual of [8388602, 8388394, 20]-code), using
- linear OOA(250, 2055, F2, 2, 9) (dual of [(2055, 2), 4060, 10]-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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(2259, 1838651, F2, 5, 19) (dual of [(1838651, 5), 9192996, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2259, 1838651, F2, 6, 19) (dual of [(1838651, 6), 11031647, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(2259, 1838651, F2, 7, 19) (dual of [(1838651, 7), 12870298, 20]-NRT-code) | [i] | ||
| 4 | Linear OOA(2259, 1838651, F2, 8, 19) (dual of [(1838651, 8), 14708949, 20]-NRT-code) | [i] | ||
| 5 | Digital (240, 259, 1838651)-net over F2 | [i] | ||