Information on Result #1307839
Linear OA(493, 1109, F4, 23) (dual of [1109, 1016, 24]-code), using 69 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 4 times 0, 1, 9 times 0, 1, 18 times 0, 1, 31 times 0) based on linear OA(486, 1033, F4, 23) (dual of [1033, 947, 24]-code), using
- construction XX applied to C1 = C([1022,20]), C2 = C([0,21]), C3 = C1 + C2 = C([0,20]), and C∩ = C1 ∩ C2 = C([1022,21]) [i] based on
- linear OA(481, 1023, F4, 22) (dual of [1023, 942, 23]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,20}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(481, 1023, F4, 22) (dual of [1023, 942, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(486, 1023, F4, 23) (dual of [1023, 937, 24]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,21}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(476, 1023, F4, 21) (dual of [1023, 947, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [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(493, 1109, F4, 2, 23) (dual of [(1109, 2), 2125, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(493, 1109, F4, 3, 23) (dual of [(1109, 3), 3234, 24]-NRT-code) | [i] | ||
| 3 | Digital (70, 93, 1109)-net over F4 | [i] | ||