Information on Result #988612
Linear OOA(4948, 2882405, F49, 3, 9) (dual of [(2882405, 3), 8647167, 10]-NRT-code), using OOA 2-folding based on linear OOA(4948, 5764810, F49, 2, 9) (dual of [(5764810, 2), 11529572, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4948, 5764811, F49, 2, 9) (dual of [(5764811, 2), 11529574, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(4914, 2882405, F49, 2, 4) (dual of [(2882405, 2), 5764796, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4914, 5764810, F49, 4) (dual of [5764810, 5764796, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(1) [i] based on
- linear OA(4913, 5764801, F49, 4) (dual of [5764801, 5764788, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(495, 5764801, F49, 2) (dual of [5764801, 5764796, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(491, 9, F49, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(1) [i] based on
- OOA 2-folding [i] based on linear OA(4914, 5764810, F49, 4) (dual of [5764810, 5764796, 5]-code), using
- linear OOA(4934, 2882406, F49, 2, 9) (dual of [(2882406, 2), 5764778, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4934, 5764812, F49, 9) (dual of [5764812, 5764778, 10]-code), using
- construction X4 applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(4933, 5764802, F49, 9) (dual of [5764802, 5764769, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802 | 498−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(4925, 5764802, F49, 7) (dual of [5764802, 5764777, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802 | 498−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(499, 10, F49, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,49)), using
- dual of repetition code with length 10 [i]
- linear OA(491, 10, F49, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, 49, F49, 1) (dual of [49, 48, 2]-code), using
- Reed–Solomon code RS(48,49) [i]
- discarding factors / shortening the dual code based on linear OA(491, 49, F49, 1) (dual of [49, 48, 2]-code), using
- construction X4 applied to C([0,4]) ⊂ C([0,3]) [i] based on
- OOA 2-folding [i] based on linear OA(4934, 5764812, F49, 9) (dual of [5764812, 5764778, 10]-code), using
- linear OOA(4914, 2882405, F49, 2, 4) (dual of [(2882405, 2), 5764796, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(796, 5764810, F7, 3, 9) (dual of [(5764810, 3), 17294334, 10]-NRT-code) | [i] | Trace Code for OOAs | |