Information on Result #1307706
Linear OA(480, 1219, F4, 19) (dual of [1219, 1139, 20]-code), using 177 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 0, 0, 0, 1, 7 times 0, 1, 16 times 0, 1, 29 times 0, 1, 46 times 0, 1, 67 times 0) based on linear OA(471, 1033, F4, 19) (dual of [1033, 962, 20]-code), using
- construction XX applied to C1 = C([1022,16]), C2 = C([0,17]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([1022,17]) [i] based on
- linear OA(466, 1023, F4, 18) (dual of [1023, 957, 19]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,16}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(466, 1023, F4, 18) (dual of [1023, 957, 19]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(471, 1023, F4, 19) (dual of [1023, 952, 20]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,17}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(461, 1023, F4, 17) (dual of [1023, 962, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [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(480, 1219, F4, 2, 19) (dual of [(1219, 2), 2358, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(480, 1219, F4, 3, 19) (dual of [(1219, 3), 3577, 20]-NRT-code) | [i] | ||
| 3 | Digital (61, 80, 1219)-net over F4 | [i] | ||