Information on Result #1084682
Linear OOA(3158, 4194832, F3, 4, 11) (dual of [(4194832, 4), 16779170, 12]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(39, 532, F3, 4, 3) (dual of [(532, 4), 2119, 4]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(39, 532, F3, 3, 3) (dual of [(532, 3), 1587, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(39, 532, F3, 2, 3) (dual of [(532, 2), 1055, 4]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(39, 532, F3, 3, 3) (dual of [(532, 3), 1587, 4]-NRT-code), using
- linear OOA(343, 2097150, F3, 4, 5) (dual of [(2097150, 4), 8388557, 6]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(343, 2391491, F3, 4, 5) (dual of [(2391491, 4), 9565921, 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, 4, 5) (dual of [(2391491, 4), 9565921, 6]-NRT-code), using
- linear OOA(3106, 2097150, F3, 4, 11) (dual of [(2097150, 4), 8388494, 12]-NRT-code), using
- OOA 4-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 4-folding [i] based on linear OA(3106, 8388600, F3, 11) (dual of [8388600, 8388494, 12]-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.