Information on Result #1315184
Linear OA(3241, 1115, F32, 18) (dual of [1115, 1074, 19]-code), using 82 step Varšamov–Edel lengthening with (ri) = (3, 1, 5 times 0, 1, 18 times 0, 1, 55 times 0) based on linear OA(3235, 1027, F32, 18) (dual of [1027, 992, 19]-code), using
- construction XX applied to C1 = C([1022,15]), C2 = C([0,16]), C3 = C1 + C2 = C([0,15]), and C∩ = C1 ∩ C2 = C([1022,16]) [i] based on
- linear OA(3233, 1023, F32, 17) (dual of [1023, 990, 18]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,15}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(3233, 1023, F32, 17) (dual of [1023, 990, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(3235, 1023, F32, 18) (dual of [1023, 988, 19]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,16}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(3231, 1023, F32, 16) (dual of [1023, 992, 17]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [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)
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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3241, 1115, F32, 2, 18) (dual of [(1115, 2), 2189, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (23, 41, 1115)-net over F32 | [i] | ||
| 3 | Linear OOA(3241, 557, F32, 2, 18) (dual of [(557, 2), 1073, 19]-NRT-code) | [i] | OOA Folding | |