Information on Result #1308230
Linear OA(4132, 1040, F4, 35) (dual of [1040, 908, 36]-code), using 6 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0) based on linear OA(4131, 1033, F4, 35) (dual of [1033, 902, 36]-code), using
- construction XX applied to C1 = C([1022,32]), C2 = C([0,33]), C3 = C1 + C2 = C([0,32]), and C∩ = C1 ∩ C2 = C([1022,33]) [i] based on
- linear OA(4126, 1023, F4, 34) (dual of [1023, 897, 35]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,32}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(4126, 1023, F4, 34) (dual of [1023, 897, 35]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,33], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(4131, 1023, F4, 35) (dual of [1023, 892, 36]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,33}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(4121, 1023, F4, 33) (dual of [1023, 902, 34]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(40, 5, F4, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(40, 5, F4, 0) (dual of [5, 5, 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(4132, 1040, F4, 2, 35) (dual of [(1040, 2), 1948, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4132, 1040, F4, 3, 35) (dual of [(1040, 3), 2988, 36]-NRT-code) | [i] | ||
| 3 | Digital (97, 132, 1040)-net over F4 | [i] | ||