Information on Result #709082
Linear OA(4208, 1070, F4, 52) (dual of [1070, 862, 53]-code), using construction XX applied to C1 = C([1018,42]), C2 = C([0,46]), C3 = C1 + C2 = C([0,42]), and C∩ = C1 ∩ C2 = C([1018,46]) based on
- linear OA(4181, 1023, F4, 48) (dual of [1023, 842, 49]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−5,−4,…,42}, and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(4176, 1023, F4, 47) (dual of [1023, 847, 48]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,46], and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(4196, 1023, F4, 52) (dual of [1023, 827, 53]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−5,−4,…,46}, and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(4161, 1023, F4, 43) (dual of [1023, 862, 44]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(47, 27, F4, 4) (dual of [27, 20, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- linear OA(45, 20, F4, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
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(4208, 535, F4, 2, 52) (dual of [(535, 2), 862, 53]-NRT-code) | [i] | OOA Folding | |