Information on Result #709046
Linear OA(4209, 1070, F4, 52) (dual of [1070, 861, 53]-code), using construction XX applied to C1 = C([1017,42]), C2 = C([0,45]), C3 = C1 + C2 = C([0,42]), and C∩ = C1 ∩ C2 = C([1017,45]) based on
- linear OA(4186, 1023, F4, 49) (dual of [1023, 837, 50]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−6,−5,…,42}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(4171, 1023, F4, 46) (dual of [1023, 852, 47]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,45], and designed minimum distance d ≥ |I|+1 = 47 [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 = {−6,−5,…,45}, 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(410, 34, F4, 5) (dual of [34, 24, 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(43, 13, F4, 2) (dual of [13, 10, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-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
None.