Information on Result #1307612
Linear OA(451, 272, F4, 16) (dual of [272, 221, 17]-code), using 3 step Varšamov–Edel lengthening with (ri) = (1, 0, 0) based on linear OA(450, 268, F4, 16) (dual of [268, 218, 17]-code), using
- construction XX applied to C1 = C([253,12]), C2 = C([0,13]), C3 = C1 + C2 = C([0,12]), and C∩ = C1 ∩ C2 = C([253,13]) [i] based on
- linear OA(445, 255, F4, 15) (dual of [255, 210, 16]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−2,−1,…,12}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(441, 255, F4, 14) (dual of [255, 214, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(449, 255, F4, 16) (dual of [255, 206, 17]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−2,−1,…,13}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(437, 255, F4, 13) (dual of [255, 218, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(41, 9, F4, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(40, 4, F4, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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(451, 272, F4, 2, 16) (dual of [(272, 2), 493, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(451, 272, F4, 3, 16) (dual of [(272, 3), 765, 17]-NRT-code) | [i] | ||
| 3 | Digital (35, 51, 272)-net over F4 | [i] | ||