Information on Result #734460
Linear OA(3217, 2052, F32, 7) (dual of [2052, 2035, 8]-code), using (u, u+v)-construction based on
- linear OA(324, 1025, F32, 3) (dual of [1025, 1021, 4]-code or 1025-cap in PG(3,32)), using
- linear OA(3213, 1027, F32, 7) (dual of [1027, 1014, 8]-code), using
- construction XX applied to C1 = C([1022,4]), C2 = C([0,5]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([1022,5]) [i] based on
- linear OA(3211, 1023, F32, 6) (dual of [1023, 1012, 7]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(3211, 1023, F32, 6) (dual of [1023, 1012, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(3213, 1023, F32, 7) (dual of [1023, 1010, 8]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,5}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(329, 1023, F32, 5) (dual of [1023, 1014, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([1022,4]), C2 = C([0,5]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([1022,5]) [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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3217, 2052, F32, 2, 7) (dual of [(2052, 2), 4087, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (10, 17, 2052)-net over F32 | [i] | ||
| 3 | Linear OA(3218, 3190, F32, 7) (dual of [3190, 3172, 8]-code) | [i] | Varšamov–Edel Lengthening | |
| 4 | Linear OOA(3217, 1026, F32, 2, 7) (dual of [(1026, 2), 2035, 8]-NRT-code) | [i] | OOA Folding | |