Information on Result #705492
Linear OA(3231, 794, F3, 53) (dual of [794, 563, 54]-code), using construction XX applied to C1 = C([722,40]), C2 = C([1,46]), C3 = C1 + C2 = C([1,40]), and C∩ = C1 ∩ C2 = C([722,46]) based on
- linear OA(3184, 728, F3, 47) (dual of [728, 544, 48]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−6,−5,…,40}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(3183, 728, F3, 46) (dual of [728, 545, 47]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(3208, 728, F3, 53) (dual of [728, 520, 54]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−6,−5,…,46}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(3159, 728, F3, 40) (dual of [728, 569, 41]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [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(310, 34, F3, 5) (dual of [34, 24, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(310, 36, F3, 5) (dual of [36, 26, 6]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- linear OA(31, 12, F3, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(33, 12, F3, 2) (dual of [12, 9, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- linear OA(36, 12, F3, 5) (dual of [12, 6, 6]-code), using
- extended Golay code Ge(3) [i]
- linear OA(31, 12, F3, 1) (dual of [12, 11, 2]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(310, 36, F3, 5) (dual of [36, 26, 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
None.