Information on Result #708399
Linear OA(4156, 1083, F4, 37) (dual of [1083, 927, 38]-code), using construction XX applied to C1 = C([319,349]), C2 = C([313,343]), C3 = C1 + C2 = C([319,343]), and C∩ = C1 ∩ C2 = C([313,349]) based on
- 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 = {319,320,…,349}, and designed minimum distance d ≥ |I|+1 = 32 [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 = {313,314,…,343}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(4136, 1023, F4, 37) (dual of [1023, 887, 38]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {313,314,…,349}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(496, 1023, F4, 25) (dual of [1023, 927, 26]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {319,320,…,343}, and designed minimum distance d ≥ |I|+1 = 26 [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(410, 30, F4, 5) (dual of [30, 20, 6]-code) (see above)
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(4157, 1084, F4, 37) (dual of [1084, 927, 38]-code) | [i] | Code Embedding in Larger Space | |