Information on Result #666483
Linear OA(2729, 756, F27, 11) (dual of [756, 727, 12]-code), using generalized (u, u+v)-construction based on
- linear OA(270, 28, F27, 0) (dual of [28, 28, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(270, 28, F27, 0) (dual of [28, 28, 1]-code) (see above)
- linear OA(270, 28, F27, 0) (dual of [28, 28, 1]-code) (see above)
- linear OA(270, 28, F27, 0) (dual of [28, 28, 1]-code) (see above)
- linear OA(270, 28, F27, 0) (dual of [28, 28, 1]-code) (see above)
- linear OA(270, 28, F27, 0) (dual of [28, 28, 1]-code) (see above)
- linear OA(270, 28, F27, 0) (dual of [28, 28, 1]-code) (see above)
- linear OA(270, 28, F27, 0) (dual of [28, 28, 1]-code) (see above)
- linear OA(270, 28, F27, 0) (dual of [28, 28, 1]-code) (see above)
- linear OA(270, 28, F27, 0) (dual of [28, 28, 1]-code) (see above)
- linear OA(270, 28, F27, 0) (dual of [28, 28, 1]-code) (see above)
- linear OA(270, 28, F27, 0) (dual of [28, 28, 1]-code) (see above)
- linear OA(270, 28, F27, 0) (dual of [28, 28, 1]-code) (see above)
- linear OA(270, 28, F27, 0) (dual of [28, 28, 1]-code) (see above)
- linear OA(270, 28, F27, 0) (dual of [28, 28, 1]-code) (see above)
- linear OA(270, 28, F27, 0) (dual of [28, 28, 1]-code) (see above)
- linear OA(271, 28, F27, 1) (dual of [28, 27, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(271, 28, F27, 1) (dual of [28, 27, 2]-code) (see above)
- linear OA(271, 28, F27, 1) (dual of [28, 27, 2]-code) (see above)
- linear OA(271, 28, F27, 1) (dual of [28, 27, 2]-code) (see above)
- linear OA(271, 28, F27, 1) (dual of [28, 27, 2]-code) (see above)
- linear OA(271, 28, F27, 1) (dual of [28, 27, 2]-code) (see above)
- linear OA(272, 28, F27, 2) (dual of [28, 26, 3]-code or 28-arc in PG(1,27)), using
- extended Reed–Solomon code RSe(26,27) [i]
- Hamming code H(2,27) [i]
- linear OA(272, 28, F27, 2) (dual of [28, 26, 3]-code or 28-arc in PG(1,27)) (see above)
- linear OA(273, 28, F27, 3) (dual of [28, 25, 4]-code or 28-arc in PG(2,27) or 28-cap in PG(2,27)), using
- extended Reed–Solomon code RSe(25,27) [i]
- oval in PG(2, 27) [i]
- linear OA(275, 28, F27, 5) (dual of [28, 23, 6]-code or 28-arc in PG(4,27)), using
- extended Reed–Solomon code RSe(23,27) [i]
- the expurgated narrow-sense BCH-code C(I) with length 28 | 272−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(2711, 28, F27, 11) (dual of [28, 17, 12]-code or 28-arc in PG(10,27)), using
- extended Reed–Solomon code RSe(17,27) [i]
- the expurgated narrow-sense BCH-code C(I) with length 28 | 272−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
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.