Information on Result #1119364
Linear OOA(3206, 4866386, F3, 5, 12) (dual of [(4866386, 5), 24331724, 13]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(328, 1594333, F3, 5, 4) (dual of [(1594333, 5), 7971637, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(328, 2391484, F3, 5, 4) (dual of [(2391484, 5), 11957392, 5]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(328, 2391485, F3, 2, 4) (dual of [(2391485, 2), 4782942, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (24, 28, 2391485)-net over F3, using
- OOA stacking with additional row [i] based on linear OOA(328, 2391485, F3, 2, 4) (dual of [(2391485, 2), 4782942, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(328, 2391484, F3, 5, 4) (dual of [(2391484, 5), 11957392, 5]-NRT-code), using
- linear OOA(358, 1594333, F3, 5, 6) (dual of [(1594333, 5), 7971607, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(358, 4782999, F3, 6) (dual of [4782999, 4782941, 7]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(3) [i] based on
- linear OA(357, 4782969, F3, 7) (dual of [4782969, 4782912, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(329, 30, F3, 29) (dual of [30, 1, 30]-code or 30-arc in PG(28,3)), using
- dual of repetition code with length 30 [i]
- linear OA(31, 30, F3, 1) (dual of [30, 29, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(6) ⊂ Ce(3) [i] based on
- OA 3-folding and stacking [i] based on linear OA(358, 4782999, F3, 6) (dual of [4782999, 4782941, 7]-code), using
- linear OOA(3120, 1677720, F3, 5, 12) (dual of [(1677720, 5), 8388480, 13]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3120, 8388600, F3, 12) (dual of [8388600, 8388480, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3120, large, F3, 12) (dual of [large, large−120, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(3120, large, F3, 12) (dual of [large, large−120, 13]-code), using
- OOA 5-folding [i] based on linear OA(3120, 8388600, F3, 12) (dual of [8388600, 8388480, 13]-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.