Information on Result #1545334
Linear OOA(4245, 57283, F4, 3, 38) (dual of [(57283, 3), 171604, 39]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4245, 57283, F4, 38) (dual of [57283, 57038, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(4245, 65609, F4, 38) (dual of [65609, 65364, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(28) [i] based on
- linear OA(4225, 65536, F4, 38) (dual of [65536, 65311, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(420, 73, F4, 8) (dual of [73, 53, 9]-code), using
- construction XX applied to C1 = C({0,1,2,3,31,47}), C2 = C([0,5]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,31,47}) [i] based on
- linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,31,47}, and minimum distance d ≥ |{−2,−1,…,4}|+1 = 8 (BCH-bound) [i]
- linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(419, 63, F4, 8) (dual of [63, 44, 9]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,31,47}, and minimum distance d ≥ |{−2,−1,…,5}|+1 = 9 (BCH-bound) [i]
- linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(41, 7, F4, 1) (dual of [7, 6, 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, 3, F4, 0) (dual of [3, 3, 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
- construction XX applied to C1 = C({0,1,2,3,31,47}), C2 = C([0,5]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,31,47}) [i] based on
- construction X applied to Ce(37) ⊂ Ce(28) [i] based on
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(4245, 8183, F4, 45, 38) (dual of [(8183, 45), 367990, 39]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |