Information on Result #1191474
Digital (102, 113, 3320494)-net over F8, using net defined by OOA based on linear OOA(8113, 3320494, F8, 15, 11) (dual of [(3320494, 15), 49807297, 12]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(8113, 6640989, F8, 3, 11) (dual of [(6640989, 3), 19922854, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8113, 6640990, F8, 3, 11) (dual of [(6640990, 3), 19922857, 12]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(831, 1048588, F8, 3, 5) (dual of [(1048588, 3), 3145733, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(82, 9, F8, 3, 2) (dual of [(9, 3), 25, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;25,8) [i]
- linear OOA(829, 1048579, F8, 3, 5) (dual of [(1048579, 3), 3145708, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(829, 2097159, F8, 5) (dual of [2097159, 2097130, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(829, 2097152, F8, 5) (dual of [2097152, 2097123, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(822, 2097152, F8, 4) (dual of [2097152, 2097130, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(80, 7, F8, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(829, 2097159, F8, 5) (dual of [2097159, 2097130, 6]-code), using
- linear OOA(82, 9, F8, 3, 2) (dual of [(9, 3), 25, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(882, 5592402, F8, 3, 11) (dual of [(5592402, 3), 16777124, 12]-NRT-code), using
- trace code [i] based on linear OOA(6441, 2796201, F64, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- trace code [i] based on linear OOA(6441, 2796201, F64, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
- linear OOA(831, 1048588, F8, 3, 5) (dual of [(1048588, 3), 3145733, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(8113, 6640990, F8, 3, 11) (dual of [(6640990, 3), 19922857, 12]-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, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.