Information on Result #702438
Linear OA(2207, 571, F2, 44) (dual of [571, 364, 45]-code), using construction XX applied to C1 = C([505,34]), C2 = C([0,38]), C3 = C1 + C2 = C([0,34]), and C∩ = C1 ∩ C2 = C([505,38]) based on
- linear OA(2172, 511, F2, 41) (dual of [511, 339, 42]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−6,−5,…,34}, and designed minimum distance d ≥ |I|+1 = 42 [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(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(2145, 511, F2, 35) (dual of [511, 366, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [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
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 OA(2209, 573, F2, 44) (dual of [573, 364, 45]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2210, 574, F2, 44) (dual of [574, 364, 45]-code) | [i] | ||
| 3 | Linear OA(2208, 572, F2, 45) (dual of [572, 364, 46]-code) | [i] | Adding a Parity Check Bit | |
| 4 | Linear OA(2211, 577, F2, 44) (dual of [577, 366, 45]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OA(2212, 579, F2, 44) (dual of [579, 367, 45]-code) | [i] | ||
| 6 | Linear OA(2213, 581, F2, 44) (dual of [581, 368, 45]-code) | [i] | ||
| 7 | Linear OA(2214, 584, F2, 44) (dual of [584, 370, 45]-code) | [i] | ||
| 8 | Linear OA(2210, 575, F2, 44) (dual of [575, 365, 45]-code) | [i] | Construction X with Varšamov Bound | |
| 9 | Linear OA(2212, 578, F2, 44) (dual of [578, 366, 45]-code) | [i] | ||
| 10 | Linear OA(2213, 580, F2, 44) (dual of [580, 367, 45]-code) | [i] | ||
| 11 | Linear OA(2214, 582, F2, 44) (dual of [582, 368, 45]-code) | [i] | ||
| 12 | Linear OOA(2207, 285, F2, 2, 44) (dual of [(285, 2), 363, 45]-NRT-code) | [i] | OOA Folding | |
| 13 | Linear OOA(2207, 190, F2, 3, 44) (dual of [(190, 3), 363, 45]-NRT-code) | [i] | ||