Information on Result #705690
Linear OA(3230, 763, F3, 57) (dual of [763, 533, 58]-code), using construction XX applied to C1 = C([337,392]), C2 = C([336,385]), C3 = C1 + C2 = C([337,385]), and C∩ = C1 ∩ C2 = C([336,392]) based on
- linear OA(3214, 728, F3, 56) (dual of [728, 514, 57]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {337,338,…,392}, and designed minimum distance d ≥ |I|+1 = 57 [i]
- linear OA(3196, 728, F3, 50) (dual of [728, 532, 51]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {336,337,…,385}, and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(3217, 728, F3, 57) (dual of [728, 511, 58]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {336,337,…,392}, and designed minimum distance d ≥ |I|+1 = 58 [i]
- linear OA(3193, 728, F3, 49) (dual of [728, 535, 50]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {337,338,…,385}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(313, 32, F3, 6) (dual of [32, 19, 7]-code), using
- construction XX applied to C1 = C({0,1,2,17}), C2 = C([0,4]), C3 = C1 + C2 = C([0,2]), and C∩ = C1 ∩ C2 = C({0,1,2,4,17}) [i] based on
- linear OA(310, 26, F3, 5) (dual of [26, 16, 6]-code), using the primitive cyclic code C(A) with length 26 = 33−1, defining set A = {0,1,2,17}, and minimum distance d ≥ |{−1,0,1,2,3}|+1 = 6 (BCH-bound) [i]
- linear OA(310, 26, F3, 5) (dual of [26, 16, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(313, 26, F3, 6) (dual of [26, 13, 7]-code), using the primitive cyclic code C(A) with length 26 = 33−1, defining set A = {0,1,2,4,17}, and minimum distance d ≥ |{−1,0,…,4}|+1 = 7 (BCH-bound) [i]
- linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(30, 3, F3, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(30, 3, F3, 0) (dual of [3, 3, 1]-code) (see above)
- construction XX applied to C1 = C({0,1,2,17}), C2 = C([0,4]), C3 = C1 + C2 = C([0,2]), and C∩ = C1 ∩ C2 = C({0,1,2,4,17}) [i] based on
- linear OA(30, 3, F3, 0) (dual of [3, 3, 1]-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
None.