MinT - Information on Result #2229941

Information on Result #2229941

Linear OA(3¹³⁸, 154, F₃, 75) (dual of [154, 16, 76]-code), using 2 times truncation based on linear OA(3¹⁴⁰, 156, F₃, 77) (dual of [156, 16, 78]-code), using

(u,Â u+v)-construction [i] based on
1. linear OA(3⁶³, 78, F₃, 38) (dual of [78, 15, 39]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁶³, 79, F₃, 38) (dual of [79, 16, 39]-code), using
    - 3 times truncation [i] based on linear OA(3⁶⁶, 82, F₃, 41) (dual of [82, 16, 42]-code), using
      - contraction [i] based on linear OA(3¹⁴⁸, 164, F₃, 83) (dual of [164, 16, 84]-code), using the BCH-code C(I) with length 164Â | 3⁸âˆ’1, defining interval IÂ =Â {0,1,…,82}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 84 [i]
2. linear OA(3⁷⁷, 78, F₃, 77) (dual of [78, 1, 78]-code or 78-arc in PG(76,3)), using
  - dual of repetition code with length 78 [i]

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:

	Result		This result only	Method
1	Linear OOA(3¹³⁸, 77, F₃, 2, 75) (dual of [(77, 2), 16, 76]-NRT-code)	[i]		OOA Folding