Information on Result #1523991
Linear OOA(3144, 4194568, F3, 3, 13) (dual of [(4194568, 3), 12583560, 14]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3144, 4194568, F3, 2, 13) (dual of [(4194568, 2), 8388992, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(323, 267, F3, 2, 6) (dual of [(267, 2), 511, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(323, 267, F3, 6) (dual of [267, 244, 7]-code), using
- 13 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 1, 9 times 0) [i] based on linear OA(321, 252, F3, 6) (dual of [252, 231, 7]-code), using
- construction XX applied to C1 = C([241,3]), C2 = C([0,4]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([241,4]) [i] based on
- linear OA(316, 242, F3, 5) (dual of [242, 226, 6]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−1,0,1,2,3}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(316, 242, F3, 5) (dual of [242, 226, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(321, 242, F3, 6) (dual of [242, 221, 7]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(311, 242, F3, 4) (dual of [242, 231, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(30, 5, F3, 0) (dual of [5, 5, 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, 5, F3, 0) (dual of [5, 5, 1]-code) (see above)
- construction XX applied to C1 = C([241,3]), C2 = C([0,4]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([241,4]) [i] based on
- 13 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 1, 9 times 0) [i] based on linear OA(321, 252, F3, 6) (dual of [252, 231, 7]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(323, 267, F3, 6) (dual of [267, 244, 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(323, 267, F3, 2, 6) (dual of [(267, 2), 511, 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(3144, 2097284, F3, 5, 13) (dual of [(2097284, 5), 10486276, 14]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3144, 2097283, F3, 15, 13) (dual of [(2097283, 15), 31459101, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |