Information on Result #677758

Linear OA(3118, 125, F3, 77) (dual of [125, 7, 78]-code), using construction XX applied to Ce(79) ⊂ Ce(52) ⊂ Ce(49) based on
  1. linear OA(380, 81, F3, 80) (dual of [81, 1, 81]-code or 81-arc in PG(79,3)), using an extension Ce(79) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,79], and designed minimum distance d ≥ |I|+1 = 80 [i]
  2. linear OA(376, 81, F3, 53) (dual of [81, 5, 54]-code), using an extension Ce(52) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [i]
  3. linear OA(374, 81, F3, 50) (dual of [81, 7, 51]-code), using an extension Ce(49) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,49], and designed minimum distance d ≥ |I|+1 = 50 [i]
  4. linear OA(334, 40, F3, 23) (dual of [40, 6, 24]-code), using
    • the expurgated narrow-sense BCH-code C(I) with length 40 | 34−1, defining interval I = [0,21], and minimum distance d ≥ |{−1,0,…,21}|+1 = 24 (BCH-bound) [i]
  5. linear OA(32, 4, F3, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), 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.

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(3118, 125, F3, 76) (dual of [125, 7, 77]-code) [i]Strength Reduction
2Linear OA(3115, 122, F3, 74) (dual of [122, 7, 75]-code) [i]Truncation
3Linear OA(3130, 137, F3, 81) (dual of [137, 7, 82]-code) [i]Juxtaposition
4Linear OA(3131, 138, F3, 82) (dual of [138, 7, 83]-code) [i]
5Linear OA(3132, 139, F3, 83) (dual of [139, 7, 84]-code) [i]
6Linear OA(3140, 147, F3, 87) (dual of [147, 7, 88]-code) [i]
7Linear OA(3141, 148, F3, 88) (dual of [148, 7, 89]-code) [i]
8Linear OA(3142, 149, F3, 89) (dual of [149, 7, 90]-code) [i]
9Linear OA(3143, 150, F3, 90) (dual of [150, 7, 91]-code) [i]
10Linear OA(3144, 151, F3, 91) (dual of [151, 7, 92]-code) [i]
11Linear OA(3145, 152, F3, 92) (dual of [152, 7, 93]-code) [i]
12Linear OA(3199, 206, F3, 128) (dual of [206, 7, 129]-code) [i]
13Linear OOA(3118, 25, F3, 5, 77) (dual of [(25, 5), 7, 78]-NRT-code) [i]OOA Folding