Information on Result #712259
Linear OA(5144, 668, F5, 42) (dual of [668, 524, 43]-code), using construction XX applied to C1 = C([618,31]), C2 = C([0,35]), C3 = C1 + C2 = C([0,31]), and C∩ = C1 ∩ C2 = C([618,35]) based on
- linear OA(5119, 624, F5, 38) (dual of [624, 505, 39]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−6,−5,…,31}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(5111, 624, F5, 36) (dual of [624, 513, 37]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,35], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(5131, 624, F5, 42) (dual of [624, 493, 43]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−6,−5,…,35}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(599, 624, F5, 32) (dual of [624, 525, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,31], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(59, 28, F5, 5) (dual of [28, 19, 6]-code), using
- construction XX applied to C1 = C({0,1,2,19}), C2 = C([0,3]), C3 = C1 + C2 = C([0,2]), and C∩ = C1 ∩ C2 = C({0,1,2,3,19}) [i] based on
- linear OA(57, 24, F5, 4) (dual of [24, 17, 5]-code), using the primitive cyclic code C(A) with length 24 = 52−1, defining set A = {0,1,2,19}, and minimum distance d ≥ |{−1,0,1,2}|+1 = 5 (BCH-bound) [i]
- linear OA(57, 24, F5, 4) (dual of [24, 17, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(59, 24, F5, 5) (dual of [24, 15, 6]-code), using the primitive cyclic code C(A) with length 24 = 52−1, defining set A = {0,1,2,3,19}, and minimum distance d ≥ |{−1,0,1,2,3}|+1 = 6 (BCH-bound) [i]
- linear OA(55, 24, F5, 3) (dual of [24, 19, 4]-code or 24-cap in PG(4,5)), using the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(50, 2, F5, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(50, 2, F5, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C({0,1,2,19}), C2 = C([0,3]), C3 = C1 + C2 = C([0,2]), and C∩ = C1 ∩ C2 = C({0,1,2,3,19}) [i] based on
- linear OA(54, 16, F5, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,5)), using
Mode: Constructive and 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(5144, 334, F5, 2, 42) (dual of [(334, 2), 524, 43]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(5144, 222, F5, 3, 42) (dual of [(222, 3), 522, 43]-NRT-code) | [i] | ||