Information on Result #1060334
Linear OOA(3200, 2097337, F3, 4, 17) (dual of [(2097337, 4), 8389148, 18]-NRT-code), using OOA 2-folding based on linear OOA(3200, 4194674, F3, 2, 17) (dual of [(4194674, 2), 8389148, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(334, 373, F3, 2, 8) (dual of [(373, 2), 712, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(334, 746, F3, 8) (dual of [746, 712, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(334, 747, F3, 8) (dual of [747, 713, 9]-code), using
- construction XX applied to C1 = C([725,3]), C2 = C([0,4]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([725,4]) [i] based on
- linear OA(325, 728, F3, 7) (dual of [728, 703, 8]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,3}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(319, 728, F3, 5) (dual of [728, 709, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(331, 728, F3, 8) (dual of [728, 697, 9]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,4}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(313, 728, F3, 4) (dual of [728, 715, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- linear OA(30, 6, F3, 0) (dual of [6, 6, 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
- construction XX applied to C1 = C([725,3]), C2 = C([0,4]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([725,4]) [i] based on
- discarding factors / shortening the dual code based on linear OA(334, 747, F3, 8) (dual of [747, 713, 9]-code), using
- OOA 2-folding [i] based on linear OA(334, 746, F3, 8) (dual of [746, 712, 9]-code), using
- linear OOA(3166, 4194301, F3, 2, 17) (dual of [(4194301, 2), 8388436, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3166, 8388602, F3, 17) (dual of [8388602, 8388436, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3166, large, F3, 17) (dual of [large, large−166, 18]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(3166, large, F3, 17) (dual of [large, large−166, 18]-code), using
- OOA 2-folding [i] based on linear OA(3166, 8388602, F3, 17) (dual of [8388602, 8388436, 18]-code), using
- linear OOA(334, 373, F3, 2, 8) (dual of [(373, 2), 712, 9]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t.
Other Results with Identical Parameters
None.
Depending Results
None.