Information on Result #1653592
Linear OOA(2238, 1677791, F2, 5, 18) (dual of [(1677791, 5), 8388717, 19]-NRT-code), using (u, u+v)-construction based on
- linear OOA(231, 71, F2, 5, 9) (dual of [(71, 5), 324, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(231, 71, F2, 2, 9) (dual of [(71, 2), 111, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(231, 142, F2, 9) (dual of [142, 111, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(231, 143, F2, 9) (dual of [143, 112, 10]-code), using
- construction XX applied to C1 = C({0,1,3,63}), C2 = C([0,5]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C({0,1,3,5,63}) [i] based on
- linear OA(222, 127, F2, 7) (dual of [127, 105, 8]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,63}, and minimum distance d ≥ |{−2,−1,…,4}|+1 = 8 (BCH-bound) [i]
- linear OA(222, 127, F2, 7) (dual of [127, 105, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(229, 127, F2, 9) (dual of [127, 98, 10]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,63}, and minimum distance d ≥ |{−2,−1,…,6}|+1 = 10 (BCH-bound) [i]
- linear OA(215, 127, F2, 5) (dual of [127, 112, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(21, 8, F2, 1) (dual of [8, 7, 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
- linear OA(21, 8, F2, 1) (dual of [8, 7, 2]-code) (see above)
- construction XX applied to C1 = C({0,1,3,63}), C2 = C([0,5]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C({0,1,3,5,63}) [i] based on
- discarding factors / shortening the dual code based on linear OA(231, 143, F2, 9) (dual of [143, 112, 10]-code), using
- OOA 2-folding [i] based on linear OA(231, 142, F2, 9) (dual of [142, 111, 10]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(231, 71, F2, 2, 9) (dual of [(71, 2), 111, 10]-NRT-code), using
- linear OOA(2207, 1677720, F2, 5, 18) (dual of [(1677720, 5), 8388393, 19]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2207, 8388600, F2, 18) (dual of [8388600, 8388393, 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 5-folding [i] based on linear OA(2207, 8388600, F2, 18) (dual of [8388600, 8388393, 19]-code), using
Mode: 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(2238, 1677791, F2, 6, 18) (dual of [(1677791, 6), 10066508, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2238, 1677791, F2, 7, 18) (dual of [(1677791, 7), 11744299, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(2238, 1677791, F2, 8, 18) (dual of [(1677791, 8), 13422090, 19]-NRT-code) | [i] | ||
| 4 | Digital (220, 238, 1677791)-net over F2 | [i] | ||