Information on Result #614648

Linear OA(750, 57, F7, 40) (dual of [57, 7, 41]-code), using the expurgated narrow-sense BCH-code C(I) with length 57 | 73−1, defining interval I = [0,29], and minimum distance d ≥ |{−10,−9,…,29}|+1 = 41 (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

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(750, 57, F7, 39) (dual of [57, 7, 40]-code) [i]Strength Reduction
2Linear OA(751, 58, F7, 40) (dual of [58, 7, 41]-code) [i]Code Embedding in Larger Space
3Linear OA(749, 56, F7, 39) (dual of [56, 7, 40]-code) [i]Truncation
4Linear OA(748, 55, F7, 38) (dual of [55, 7, 39]-code) [i]
5Linear OA(747, 54, F7, 37) (dual of [54, 7, 38]-code) [i]
6Linear OA(746, 53, F7, 36) (dual of [53, 7, 37]-code) [i]
7Linear OA(745, 52, F7, 35) (dual of [52, 7, 36]-code) [i]
8Linear OA(7106, 112, F7, 81) (dual of [112, 6, 82]-code) [i]Repeating Each Code Word
9Linear OA(7105, 110, F7, 81) (dual of [110, 5, 82]-code) [i]
10Linear OA(757, 64, F7, 41) (dual of [64, 7, 42]-code) [i]Juxtaposition
11Linear OA(758, 65, F7, 42) (dual of [65, 7, 43]-code) [i]
12Linear OA(760, 67, F7, 43) (dual of [67, 7, 44]-code) [i]
13Linear OA(761, 68, F7, 44) (dual of [68, 7, 45]-code) [i]
14Linear OA(763, 70, F7, 45) (dual of [70, 7, 46]-code) [i]
15Linear OA(764, 71, F7, 46) (dual of [71, 7, 47]-code) [i]
16Linear OA(765, 72, F7, 47) (dual of [72, 7, 48]-code) [i]
17Linear OA(766, 73, F7, 48) (dual of [73, 7, 49]-code) [i]
18Linear OA(767, 74, F7, 49) (dual of [74, 7, 50]-code) [i]
19Linear OA(770, 77, F7, 50) (dual of [77, 7, 51]-code) [i]
20Linear OA(771, 78, F7, 51) (dual of [78, 7, 52]-code) [i]
21Linear OA(772, 79, F7, 52) (dual of [79, 7, 53]-code) [i]
22Linear OA(773, 80, F7, 53) (dual of [80, 7, 54]-code) [i]
23Linear OA(775, 82, F7, 54) (dual of [82, 7, 55]-code) [i]
24Linear OA(792, 99, F7, 68) (dual of [99, 7, 69]-code) [i]
25Linear OA(793, 100, F7, 69) (dual of [100, 7, 70]-code) [i]
26Linear OA(794, 101, F7, 70) (dual of [101, 7, 71]-code) [i]
27Linear OA(795, 102, F7, 71) (dual of [102, 7, 72]-code) [i]
28Linear OA(796, 103, F7, 72) (dual of [103, 7, 73]-code) [i]
29Linear OA(797, 104, F7, 73) (dual of [104, 7, 74]-code) [i]
30Linear OA(798, 105, F7, 74) (dual of [105, 7, 75]-code) [i]
31Linear OA(7100, 107, F7, 75) (dual of [107, 7, 76]-code) [i]
32Linear OA(7110, 117, F7, 82) (dual of [117, 7, 83]-code) [i]
33Linear OA(760, 68, F7, 40) (dual of [68, 8, 41]-code) [i]✔Construction X with Cyclic Codes
34Linear OA(758, 68, F7, 40) (dual of [68, 10, 41]-code) [i]✔
35Linear OA(755, 65, F7, 38) (dual of [65, 10, 39]-code) [i]✔
36Linear OA(757, 64, F7, 42) (dual of [64, 7, 43]-code) [i]✔
37Linear OA(777, 84, F7, 56) (dual of [84, 7, 57]-code) [i]✔
38Linear OA(775, 82, F7, 55) (dual of [82, 7, 56]-code) [i]✔
39Linear OA(772, 79, F7, 53) (dual of [79, 7, 54]-code) [i]✔
40Linear OA(766, 73, F7, 49) (dual of [73, 7, 50]-code) [i]✔
41Linear OA(761, 68, F7, 45) (dual of [68, 7, 46]-code) [i]✔
42Linear OA(758, 65, F7, 43) (dual of [65, 7, 44]-code) [i]✔
43Linear OA(768, 75, F7, 50) (dual of [75, 7, 51]-code) [i]✔
44Linear OA(756, 63, F7, 42) (dual of [63, 7, 43]-code) [i]✔Construction XX with Cyclic Codes
45Linear OOA(750, 28, F7, 2, 40) (dual of [(28, 2), 6, 41]-NRT-code) [i]OOA Folding
46Linear OOA(750, 19, F7, 3, 40) (dual of [(19, 3), 7, 41]-NRT-code) [i]