Information on Result #2274411
Linear OA(4242, 1074, F4, 61) (dual of [1074, 832, 62]-code), using 1 times code embedding in larger space based on linear OA(4241, 1073, F4, 61) (dual of [1073, 832, 62]-code), using
- construction XX applied to C1 = C([293,349]), C2 = C([289,343]), C3 = C1 + C2 = C([293,343]), and C∩ = C1 ∩ C2 = C([289,349]) [i] based on
- linear OA(4211, 1023, F4, 57) (dual of [1023, 812, 58]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {293,294,…,349}, and designed minimum distance d ≥ |I|+1 = 58 [i]
- linear OA(4206, 1023, F4, 55) (dual of [1023, 817, 56]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {289,290,…,343}, and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(4226, 1023, F4, 61) (dual of [1023, 797, 62]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {289,290,…,349}, and designed minimum distance d ≥ |I|+1 = 62 [i]
- linear OA(4191, 1023, F4, 51) (dual of [1023, 832, 52]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {293,294,…,343}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(410, 30, F4, 5) (dual of [30, 20, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-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(4242, 537, F4, 2, 61) (dual of [(537, 2), 832, 62]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4242, 358, F4, 3, 61) (dual of [(358, 3), 832, 62]-NRT-code) | [i] | ||