Information on Result #703703

Linear OA(3243, 275, F3, 133) (dual of [275, 32, 134]-code), using construction XX applied to C1 = C([233,120]), C2 = C([1,124]), C3 = C1 + C2 = C([1,120]), and C∩ = C1 ∩ C2 = C([233,124]) based on
  1. linear OA(3221, 242, F3, 130) (dual of [242, 21, 131]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−9,−8,…,120}, and designed minimum distance d ≥ |I|+1 = 131 [i]
  2. linear OA(3216, 242, F3, 124) (dual of [242, 26, 125]-code), using the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,124], and designed minimum distance d ≥ |I|+1 = 125 [i]
  3. linear OA(3227, 242, F3, 134) (dual of [242, 15, 135]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−9,−8,…,124}, and designed minimum distance d ≥ |I|+1 = 135 [i]
  4. linear OA(3210, 242, F3, 120) (dual of [242, 32, 121]-code), using the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,120], and designed minimum distance d ≥ |I|+1 = 121 [i]
  5. linear OA(312, 23, F3, 8) (dual of [23, 11, 9]-code), using
  6. linear OA(34, 10, F3, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,3)), 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:

ResultThis
result
only		Method
1Linear OA(3243, 275, F3, 132) (dual of [275, 32, 133]-code) [i]Strength Reduction
2Linear OA(3243, 275, F3, 131) (dual of [275, 32, 132]-code) [i]
3Linear OA(3243, 275, F3, 130) (dual of [275, 32, 131]-code) [i]
4Linear OA(3243, 275, F3, 129) (dual of [275, 32, 130]-code) [i]
5Linear OA(3243, 275, F3, 128) (dual of [275, 32, 129]-code) [i]
6Linear OA(3243, 275, F3, 127) (dual of [275, 32, 128]-code) [i]
7Linear OA(3243, 275, F3, 126) (dual of [275, 32, 127]-code) [i]
8Linear OA(3243, 275, F3, 125) (dual of [275, 32, 126]-code) [i]
9Linear OA(3243, 275, F3, 124) (dual of [275, 32, 125]-code) [i]
10Linear OA(3243, 275, F3, 123) (dual of [275, 32, 124]-code) [i]
11Linear OA(3244, 276, F3, 133) (dual of [276, 32, 134]-code) [i]Code Embedding in Larger Space
12Linear OA(3245, 277, F3, 133) (dual of [277, 32, 134]-code) [i]
13Linear OA(3246, 278, F3, 133) (dual of [278, 32, 134]-code) [i]
14Linear OA(3250, 282, F3, 133) (dual of [282, 32, 134]-code) [i]
15Linear OA(3242, 274, F3, 132) (dual of [274, 32, 133]-code) [i]Truncation
16Linear OA(3241, 273, F3, 131) (dual of [273, 32, 132]-code) [i]
17Linear OA(3239, 271, F3, 129) (dual of [271, 32, 130]-code) [i]
18Linear OA(3238, 270, F3, 128) (dual of [270, 32, 129]-code) [i]
19Linear OA(3237, 269, F3, 127) (dual of [269, 32, 128]-code) [i]
20Linear OA(3236, 268, F3, 126) (dual of [268, 32, 127]-code) [i]
21Linear OA(3233, 265, F3, 123) (dual of [265, 32, 124]-code) [i]
22Linear OA(3232, 264, F3, 122) (dual of [264, 32, 123]-code) [i]
23Linear OA(3229, 261, F3, 119) (dual of [261, 32, 120]-code) [i]
24Linear OA(3226, 258, F3, 116) (dual of [258, 32, 117]-code) [i]
25Linear OA(3225, 257, F3, 115) (dual of [257, 32, 116]-code) [i]
26Linear OA(3224, 256, F3, 114) (dual of [256, 32, 115]-code) [i]
27Linear OA(3223, 255, F3, 113) (dual of [255, 32, 114]-code) [i]
28Linear OA(3222, 254, F3, 112) (dual of [254, 32, 113]-code) [i]
29Linear OA(3220, 252, F3, 110) (dual of [252, 32, 111]-code) [i]
30Linear OA(3217, 249, F3, 107) (dual of [249, 32, 108]-code) [i]
31Linear OA(3216, 248, F3, 106) (dual of [248, 32, 107]-code) [i]
32Linear OA(3215, 247, F3, 105) (dual of [247, 32, 106]-code) [i]
33Linear OA(3214, 246, F3, 104) (dual of [246, 32, 105]-code) [i]
34Linear OA(3213, 245, F3, 103) (dual of [245, 32, 104]-code) [i]
35Linear OOA(3243, 137, F3, 2, 133) (dual of [(137, 2), 31, 134]-NRT-code) [i]OOA Folding
36Linear OOA(3243, 55, F3, 5, 133) (dual of [(55, 5), 32, 134]-NRT-code) [i]