Information on Result #1117176
Linear OOA(3139, 1753763, F3, 5, 11) (dual of [(1753763, 5), 8768676, 12]-NRT-code), using (u, u+v)-construction based on
- linear OOA(340, 797167, F3, 5, 5) (dual of [(797167, 5), 3985795, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(340, 1594335, F3, 5) (dual of [1594335, 1594295, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(340, 1594336, F3, 5) (dual of [1594336, 1594296, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(340, 1594323, F3, 5) (dual of [1594323, 1594283, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(327, 1594323, F3, 4) (dual of [1594323, 1594296, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(30, 13, F3, 0) (dual of [13, 13, 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
- discarding factors / shortening the dual code based on linear OA(340, 1594336, F3, 5) (dual of [1594336, 1594296, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(340, 1594335, F3, 5) (dual of [1594335, 1594295, 6]-code), using
- linear OOA(399, 956596, F3, 5, 11) (dual of [(956596, 5), 4782881, 12]-NRT-code), using
- OOA 5-folding [i] based on linear OA(399, 4782980, F3, 11) (dual of [4782980, 4782881, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(399, 4782983, F3, 11) (dual of [4782983, 4782884, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(399, 4782969, F3, 11) (dual of [4782969, 4782870, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(385, 4782969, F3, 10) (dual of [4782969, 4782884, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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 (see above)
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(399, 4782983, F3, 11) (dual of [4782983, 4782884, 12]-code), using
- OOA 5-folding [i] based on linear OA(399, 4782980, F3, 11) (dual of [4782980, 4782881, 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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3139, 1753762, F3, 15, 11) (dual of [(1753762, 15), 26306291, 12]-NRT-code) | [i] | OOA Stacking with Additional Row | |