Information on Result #1060333
Linear OOA(3199, 2097336, F3, 4, 17) (dual of [(2097336, 4), 8389145, 18]-NRT-code), using OOA 2-folding based on linear OOA(3199, 4194672, F3, 2, 17) (dual of [(4194672, 2), 8389145, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(333, 371, F3, 2, 8) (dual of [(371, 2), 709, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(333, 742, F3, 8) (dual of [742, 709, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(333, 743, F3, 8) (dual of [743, 710, 9]-code), using
- construction XX applied to C1 = C([727,4]), C2 = C([1,6]), C3 = C1 + C2 = C([1,4]), and C∩ = C1 ∩ C2 = C([727,6]) [i] based on
- linear OA(325, 728, F3, 6) (dual of [728, 703, 7]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(324, 728, F3, 6) (dual of [728, 704, 7]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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 = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(318, 728, F3, 4) (dual of [728, 710, 5]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(31, 8, F3, 1) (dual of [8, 7, 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(31, 7, F3, 1) (dual of [7, 6, 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 (see above)
- construction XX applied to C1 = C([727,4]), C2 = C([1,6]), C3 = C1 + C2 = C([1,4]), and C∩ = C1 ∩ C2 = C([727,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(333, 743, F3, 8) (dual of [743, 710, 9]-code), using
- OOA 2-folding [i] based on linear OA(333, 742, F3, 8) (dual of [742, 709, 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(333, 371, F3, 2, 8) (dual of [(371, 2), 709, 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.