Information on Result #700690

Linear OA(313, 32, F3, 6) (dual of [32, 19, 7]-code), using construction XX applied to C1 = C({0,1,2,17}), C2 = C([0,4]), C3 = C1 + C2 = C([0,2]), and C∩ = C1 ∩ C2 = C({0,1,2,4,17}) based on
  1. linear OA(310, 26, F3, 5) (dual of [26, 16, 6]-code), using the primitive cyclic code C(A) with length 26 = 33−1, defining set A = {0,1,2,17}, and minimum distance d ≥ |{−1,0,1,2,3}|+1 = 6 (BCH-bound) [i]
  2. linear OA(310, 26, F3, 5) (dual of [26, 16, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
  3. linear OA(313, 26, F3, 6) (dual of [26, 13, 7]-code), using the primitive cyclic code C(A) with length 26 = 33−1, defining set A = {0,1,2,4,17}, and minimum distance d ≥ |{−1,0,…,4}|+1 = 7 (BCH-bound) [i]
  4. linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
  5. linear OA(30, 3, F3, 0) (dual of [3, 3, 1]-code), using
  6. linear OA(30, 3, F3, 0) (dual of [3, 3, 1]-code) (see above)

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(3130, 281, F3, 39) (dual of [281, 151, 40]-code) [i]Construction XX with Cyclic Codes
2Linear OA(3129, 279, F3, 39) (dual of [279, 150, 40]-code) [i]
3Linear OA(3137, 287, F3, 41) (dual of [287, 150, 42]-code) [i]
4Linear OA(3135, 280, F3, 41) (dual of [280, 145, 42]-code) [i]
5Linear OA(3154, 780, F3, 35) (dual of [780, 626, 36]-code) [i]
6Linear OA(3166, 780, F3, 38) (dual of [780, 614, 39]-code) [i]
7Linear OA(3174, 785, F3, 40) (dual of [785, 611, 41]-code) [i]
8Linear OA(3183, 794, F3, 41) (dual of [794, 611, 42]-code) [i]
9Linear OA(3179, 784, F3, 41) (dual of [784, 605, 42]-code) [i]
10Linear OA(3189, 794, F3, 43) (dual of [794, 605, 44]-code) [i]
11Linear OA(3186, 785, F3, 43) (dual of [785, 599, 44]-code) [i]
12Linear OA(3195, 794, F3, 44) (dual of [794, 599, 45]-code) [i]
13Linear OA(3191, 784, F3, 44) (dual of [784, 593, 45]-code) [i]
14Linear OA(3201, 794, F3, 46) (dual of [794, 593, 47]-code) [i]
15Linear OA(3198, 785, F3, 46) (dual of [785, 587, 47]-code) [i]
16Linear OA(3207, 794, F3, 47) (dual of [794, 587, 48]-code) [i]
17Linear OA(3203, 784, F3, 47) (dual of [784, 581, 48]-code) [i]
18Linear OA(3213, 794, F3, 49) (dual of [794, 581, 50]-code) [i]
19Linear OA(3210, 785, F3, 49) (dual of [785, 575, 50]-code) [i]
20Linear OA(3219, 794, F3, 50) (dual of [794, 575, 51]-code) [i]
21Linear OA(3215, 784, F3, 50) (dual of [784, 569, 51]-code) [i]
22Linear OA(3225, 794, F3, 52) (dual of [794, 569, 53]-code) [i]
23Linear OA(3222, 785, F3, 52) (dual of [785, 563, 53]-code) [i]
24Linear OA(3231, 794, F3, 53) (dual of [794, 563, 54]-code) [i]
25Linear OA(3227, 784, F3, 53) (dual of [784, 557, 54]-code) [i]
26Linear OA(3237, 794, F3, 55) (dual of [794, 557, 56]-code) [i]
27Linear OA(3234, 785, F3, 55) (dual of [785, 551, 56]-code) [i]
28Linear OA(3230, 763, F3, 57) (dual of [763, 533, 58]-code) [i]
29Linear OA(3237, 767, F3, 59) (dual of [767, 530, 60]-code) [i]
30Linear OA(3243, 768, F3, 60) (dual of [768, 525, 61]-code) [i]
31Linear OA(3242, 766, F3, 60) (dual of [766, 524, 61]-code) [i]
32Linear OA(3247, 778, F3, 60) (dual of [778, 531, 61]-code) [i]
33Linear OA(3247, 780, F3, 60) (dual of [780, 533, 61]-code) [i]
34Linear OA(3249, 767, F3, 62) (dual of [767, 518, 63]-code) [i]