Information on Result #2260679
Linear OA(2227, 573, F2, 49) (dual of [573, 346, 50]-code), using 1 times code embedding in larger space based on linear OA(2226, 572, F2, 49) (dual of [572, 346, 50]-code), using
- adding a parity check bit [i] based on linear OA(2225, 571, F2, 48) (dual of [571, 346, 49]-code), using
- construction XX applied to C1 = C([505,38]), C2 = C([0,42]), C3 = C1 + C2 = C([0,38]), and C∩ = C1 ∩ C2 = C([505,42]) [i] based on
- linear OA(2190, 511, F2, 45) (dual of [511, 321, 46]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−6,−5,…,38}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(2181, 511, F2, 43) (dual of [511, 330, 44]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(2208, 511, F2, 49) (dual of [511, 303, 50]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−6,−5,…,42}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(2163, 511, F2, 39) (dual of [511, 348, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(211, 36, F2, 4) (dual of [36, 25, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(211, 44, F2, 4) (dual of [44, 33, 5]-code), using
- linear OA(26, 24, F2, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction XX applied to C1 = C([505,38]), C2 = C([0,42]), C3 = C1 + C2 = C([0,38]), and C∩ = C1 ∩ C2 = C([505,42]) [i] based on
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(2227, 191, F2, 3, 49) (dual of [(191, 3), 346, 50]-NRT-code) | [i] | OOA Folding | |