Information on Result #677840

Linear OA(314, 31, F3, 7) (dual of [31, 17, 8]-code), using construction X applied to Ce(6) ⊂ Ce(4) based on
  1. linear OA(313, 27, F3, 7) (dual of [27, 14, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
  2. linear OA(310, 27, F3, 5) (dual of [27, 17, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
  3. linear OA(31, 4, F3, 1) (dual of [4, 3, 2]-code), 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.

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(3105, 273, F3, 30) (dual of [273, 168, 31]-code) [i]Construction X with Cyclic Codes
2Linear OA(3105, 274, F3, 30) (dual of [274, 169, 31]-code) [i]Construction XX with Cyclic Codes
3Linear OA(3118, 286, F3, 33) (dual of [286, 168, 34]-code) [i]
4Linear OA(3128, 286, F3, 36) (dual of [286, 158, 37]-code) [i]
5Linear OA(3135, 278, F3, 41) (dual of [278, 143, 42]-code) [i]
6Linear OA(3238, 767, F3, 59) (dual of [767, 529, 60]-code) [i]
7Linear OA(3237, 765, F3, 59) (dual of [765, 528, 60]-code) [i]
8Linear OA(3248, 777, F3, 61) (dual of [777, 529, 62]-code) [i]
9Linear OA(3247, 775, F3, 61) (dual of [775, 528, 62]-code) [i]
10Linear OA(3244, 772, F3, 60) (dual of [772, 528, 61]-code) [i]
11Linear OA(3244, 766, F3, 61) (dual of [766, 522, 62]-code) [i]
12Linear OA(3107, 276, F3, 31) (dual of [276, 169, 32]-code) [i]Construction XX with a Chain of Extended Narrow-Sense BCH Codes