Information on Result #1183566
Digital (163, 174, 5033171)-net over F3, using net defined by OOA based on linear OOA(3174, 5033171, F3, 15, 11) (dual of [(5033171, 15), 75497391, 12]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(3174, 5033172, F3, 5, 11) (dual of [(5033172, 5), 25165686, 12]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(320, 1677724, F3, 5, 3) (dual of [(1677724, 5), 8388600, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(320, 3713024, F3, 5, 3) (dual of [(3713024, 5), 18565100, 4]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(320, 3713024, F3, 3, 3) (dual of [(3713024, 3), 11139052, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(320, 3713024, F3, 2, 3) (dual of [(3713024, 2), 7426028, 4]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(320, 3713024, F3, 3, 3) (dual of [(3713024, 3), 11139052, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(320, 3713024, F3, 5, 3) (dual of [(3713024, 5), 18565100, 4]-NRT-code), using
- linear OOA(343, 1677724, F3, 5, 5) (dual of [(1677724, 5), 8388577, 6]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(343, 2391491, F3, 5, 5) (dual of [(2391491, 5), 11957412, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(343, 4782983, F3, 5) (dual of [4782983, 4782940, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(343, 4782969, F3, 5) (dual of [4782969, 4782926, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(329, 4782969, F3, 4) (dual of [4782969, 4782940, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(30, 14, F3, 0) (dual of [14, 14, 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 X applied to Ce(4) ⊂ Ce(3) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(343, 4782983, F3, 5) (dual of [4782983, 4782940, 6]-code), using
- discarding factors / shortening the dual code based on linear OOA(343, 2391491, F3, 5, 5) (dual of [(2391491, 5), 11957412, 6]-NRT-code), using
- linear OOA(3111, 1677724, F3, 5, 11) (dual of [(1677724, 5), 8388509, 12]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(35, 4, F3, 5, 5) (dual of [(4, 5), 15, 6]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(5;15,3) [i]
- linear OOA(3106, 1677720, F3, 5, 11) (dual of [(1677720, 5), 8388494, 12]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3106, 8388600, F3, 11) (dual of [8388600, 8388494, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(3106, large, F3, 11) (dual of [large, large−106, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(3106, large, F3, 11) (dual of [large, large−106, 12]-code), using
- OOA 5-folding [i] based on linear OA(3106, 8388600, F3, 11) (dual of [8388600, 8388494, 12]-code), using
- linear OOA(35, 4, F3, 5, 5) (dual of [(4, 5), 15, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(320, 1677724, F3, 5, 3) (dual of [(1677724, 5), 8388600, 4]-NRT-code), using
- generalized (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, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.