Information on Result #1202410
Digital (54, 67, 1486675)-net over F81, using net defined by OOA based on linear OOA(8167, 1486675, F81, 14, 13) (dual of [(1486675, 14), 20813383, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(8167, 4460026, F81, 2, 13) (dual of [(4460026, 2), 8919985, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8167, 4460027, F81, 2, 13) (dual of [(4460027, 2), 8919987, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(8118, 265726, F81, 2, 6) (dual of [(265726, 2), 531434, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8118, 531452, F81, 6) (dual of [531452, 531434, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(2) [i] based on
- linear OA(8116, 531441, F81, 6) (dual of [531441, 531425, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(817, 531441, F81, 3) (dual of [531441, 531434, 4]-code or 531441-cap in PG(6,81)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(812, 11, F81, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,81)), using
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
- Reed–Solomon code RS(79,81) [i]
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
- construction X applied to Ce(5) ⊂ Ce(2) [i] based on
- OOA 2-folding [i] based on linear OA(8118, 531452, F81, 6) (dual of [531452, 531434, 7]-code), using
- linear OOA(8149, 4194301, F81, 2, 13) (dual of [(4194301, 2), 8388553, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8149, 8388602, F81, 13) (dual of [8388602, 8388553, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(8149, large, F81, 13) (dual of [large, large−49, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8149, large, F81, 13) (dual of [large, large−49, 14]-code), using
- OOA 2-folding [i] based on linear OA(8149, 8388602, F81, 13) (dual of [8388602, 8388553, 14]-code), using
- linear OOA(8118, 265726, F81, 2, 6) (dual of [(265726, 2), 531434, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(8167, 4460027, F81, 2, 13) (dual of [(4460027, 2), 8919987, 14]-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.