Information on Result #708406
Linear OA(4164, 1090, F4, 38) (dual of [1090, 926, 39]-code), using construction XX applied to C1 = C([309,340]), C2 = C([316,346]), C3 = C1 + C2 = C([316,340]), and C∩ = C1 ∩ C2 = C([309,346]) based on
- linear OA(4120, 1023, F4, 32) (dual of [1023, 903, 33]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {309,310,…,340}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(4116, 1023, F4, 31) (dual of [1023, 907, 32]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {316,317,…,346}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(4141, 1023, F4, 38) (dual of [1023, 882, 39]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {309,310,…,346}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(495, 1023, F4, 25) (dual of [1023, 928, 26]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {316,317,…,340}, and designed minimum distance d ≥ |I|+1 = 26 [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, 31, F4, 5) (dual of [31, 21, 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 OA(4165, 1091, F4, 38) (dual of [1091, 926, 39]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4164, 545, F4, 2, 38) (dual of [(545, 2), 926, 39]-NRT-code) | [i] | OOA Folding | |