Information on Result #1523651
Linear OOA(3138, 4194388, F3, 3, 13) (dual of [(4194388, 3), 12583026, 14]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3138, 4194388, F3, 2, 13) (dual of [(4194388, 2), 8388638, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(317, 87, F3, 2, 6) (dual of [(87, 2), 157, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(317, 87, F3, 6) (dual of [87, 70, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(317, 88, F3, 6) (dual of [88, 71, 7]-code), using
- construction XX applied to C1 = C({0,1,2,53}), C2 = C([0,4]), C3 = C1 + C2 = C([0,2]), and C∩ = C1 ∩ C2 = C({0,1,2,4,53}) [i] based on
- linear OA(313, 80, F3, 5) (dual of [80, 67, 6]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,53}, and minimum distance d ≥ |{−1,0,1,2,3}|+1 = 6 (BCH-bound) [i]
- linear OA(313, 80, F3, 5) (dual of [80, 67, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(317, 80, F3, 6) (dual of [80, 63, 7]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,53}, and minimum distance d ≥ |{−1,0,…,4}|+1 = 7 (BCH-bound) [i]
- linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(30, 4, F3, 0) (dual of [4, 4, 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
- linear OA(30, 4, F3, 0) (dual of [4, 4, 1]-code) (see above)
- construction XX applied to C1 = C({0,1,2,53}), C2 = C([0,4]), C3 = C1 + C2 = C([0,2]), and C∩ = C1 ∩ C2 = C({0,1,2,4,53}) [i] based on
- discarding factors / shortening the dual code based on linear OA(317, 88, F3, 6) (dual of [88, 71, 7]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(317, 87, F3, 6) (dual of [87, 70, 7]-code), using
- linear OOA(3121, 4194301, F3, 2, 13) (dual of [(4194301, 2), 8388481, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3121, 8388602, F3, 13) (dual of [8388602, 8388481, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(3121, large, F3, 13) (dual of [large, large−121, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, 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(3121, large, F3, 13) (dual of [large, large−121, 14]-code), using
- OOA 2-folding [i] based on linear OA(3121, 8388602, F3, 13) (dual of [8388602, 8388481, 14]-code), using
- linear OOA(317, 87, F3, 2, 6) (dual of [(87, 2), 157, 7]-NRT-code), using
Mode: 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(3138, 2097194, F3, 5, 13) (dual of [(2097194, 5), 10485832, 14]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3138, 2097193, F3, 15, 13) (dual of [(2097193, 15), 31457757, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |