Information on Result #708177
Linear OA(4144, 1089, F4, 33) (dual of [1089, 945, 34]-code), using construction XX applied to C1 = C([323,349]), C2 = C([317,342]), C3 = C1 + C2 = C([323,342]), and C∩ = C1 ∩ C2 = C([317,349]) based on
- linear OA(4101, 1023, F4, 27) (dual of [1023, 922, 28]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {323,324,…,349}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(496, 1023, F4, 26) (dual of [1023, 927, 27]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {317,318,…,342}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(4121, 1023, F4, 33) (dual of [1023, 902, 34]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {317,318,…,349}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(476, 1023, F4, 20) (dual of [1023, 947, 21]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {323,324,…,342}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(413, 36, F4, 6) (dual of [36, 23, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- 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
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(4144, 544, F4, 2, 33) (dual of [(544, 2), 944, 34]-NRT-code) | [i] | OOA Folding | |