Information on Result #614593

Linear OA(741, 50, F7, 33) (dual of [50, 9, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 50 | 74−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound)

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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(741, 50, F7, 32) (dual of [50, 9, 33]-code) [i]Strength Reduction
2Linear OA(741, 50, F7, 31) (dual of [50, 9, 32]-code) [i]
3Linear OA(741, 50, F7, 30) (dual of [50, 9, 31]-code) [i]
4Linear OA(742, 51, F7, 33) (dual of [51, 9, 34]-code) [i]Code Embedding in Larger Space
5Linear OA(738, 47, F7, 30) (dual of [47, 9, 31]-code) [i]Truncation
6Linear OA(737, 46, F7, 29) (dual of [46, 9, 30]-code) [i]
7Linear OA(736, 45, F7, 28) (dual of [45, 9, 29]-code) [i]
8Linear OA(735, 44, F7, 27) (dual of [44, 9, 28]-code) [i]
9Linear OA(734, 43, F7, 26) (dual of [43, 9, 27]-code) [i]
10Linear OA(733, 42, F7, 25) (dual of [42, 9, 26]-code) [i]
11Linear OA(732, 41, F7, 24) (dual of [41, 9, 25]-code) [i]
12Linear OA(731, 40, F7, 23) (dual of [40, 9, 24]-code) [i]
13Linear OA(730, 39, F7, 22) (dual of [39, 9, 23]-code) [i]
14Linear OA(791, 100, F7, 67) (dual of [100, 9, 68]-code) [i]Repeating Each Code Word
15Linear OA(750, 59, F7, 34) (dual of [59, 9, 35]-code) [i]Juxtaposition
16Linear OA(751, 60, F7, 35) (dual of [60, 9, 36]-code) [i]
17Linear OA(753, 62, F7, 36) (dual of [62, 9, 37]-code) [i]
18Linear OA(754, 63, F7, 37) (dual of [63, 9, 38]-code) [i]
19Linear OA(756, 65, F7, 38) (dual of [65, 9, 39]-code) [i]
20Linear OA(757, 66, F7, 39) (dual of [66, 9, 40]-code) [i]
21Linear OA(758, 67, F7, 40) (dual of [67, 9, 41]-code) [i]
22Linear OA(759, 68, F7, 41) (dual of [68, 9, 42]-code) [i]
23Linear OA(760, 69, F7, 42) (dual of [69, 9, 43]-code) [i]
24Linear OA(763, 72, F7, 43) (dual of [72, 9, 44]-code) [i]
25Linear OA(764, 73, F7, 44) (dual of [73, 9, 45]-code) [i]
26Linear OA(765, 74, F7, 45) (dual of [74, 9, 46]-code) [i]
27Linear OA(766, 75, F7, 46) (dual of [75, 9, 47]-code) [i]
28Linear OA(771, 80, F7, 48) (dual of [80, 9, 49]-code) [i]
29Linear OA(7102, 111, F7, 73) (dual of [111, 9, 74]-code) [i]
30Linear OA(772, 81, F7, 50) (dual of [81, 9, 51]-code) [i]
31Linear OA(773, 82, F7, 51) (dual of [82, 9, 52]-code) [i]
32Linear OA(775, 84, F7, 52) (dual of [84, 9, 53]-code) [i]
33Linear OA(776, 85, F7, 53) (dual of [85, 9, 54]-code) [i]
34Linear OA(777, 86, F7, 54) (dual of [86, 9, 55]-code) [i]
35Linear OA(778, 87, F7, 55) (dual of [87, 9, 56]-code) [i]
36Linear OA(779, 88, F7, 56) (dual of [88, 9, 57]-code) [i]
37Linear OA(7103, 112, F7, 74) (dual of [112, 9, 75]-code) [i]
38Linear OA(749, 59, F7, 33) (dual of [59, 10, 34]-code) [i]✔Construction X with Cyclic Codes
39Linear OA(746, 55, F7, 35) (dual of [55, 9, 36]-code) [i]✔
40Linear OA(771, 80, F7, 49) (dual of [80, 9, 50]-code) [i]✔
41Linear OA(767, 76, F7, 47) (dual of [76, 9, 48]-code) [i]✔
42Linear OA(765, 74, F7, 46) (dual of [74, 9, 47]-code) [i]✔
43Linear OA(759, 68, F7, 42) (dual of [68, 9, 43]-code) [i]✔
44Linear OA(756, 73, F7, 33) (dual of [73, 17, 34]-code) [i]✔
45Linear OA(751, 68, F7, 30) (dual of [68, 17, 31]-code) [i]✔
46Linear OA(757, 78, F7, 32) (dual of [78, 21, 33]-code) [i]✔
47Linear OA(770, 79, F7, 49) (dual of [79, 9, 50]-code) [i]✔
48Linear OA(768, 77, F7, 48) (dual of [77, 9, 49]-code) [i]✔
49Linear OOA(741, 25, F7, 2, 33) (dual of [(25, 2), 9, 34]-NRT-code) [i]OOA Folding