MinT - Information on Result #2238383

Information on Result #2238383

Linear OA(4¹⁷¹, 180, F₄, 116) (dual of [180, 9, 117]-code), using 9 times truncation based on linear OA(4¹⁸⁰, 189, F₄, 125) (dual of [189, 9, 126]-code), using

(u,Â uâˆ’v,Â u+v+w)-construction [i] based on
1. linear OA(4⁵⁵, 63, F₄, 41) (dual of [63, 8, 42]-code), using
  - 2 times truncation [i] based on linear OA(4⁵⁷, 65, F₄, 43) (dual of [65, 8, 44]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 65Â | 4⁶âˆ’1, defining interval IÂ =Â [0,21], and minimum distance dÂ â‰¥ |{−21,−20,…,21}|+1Â =Â 44 (BCH-bound) [i]
2. linear OA(4⁶², 63, F₄, 62) (dual of [63, 1, 63]-code or 63-arc in PG(61,4)), using
  - dual of repetition code with length 63 [i]
3. linear OA(4⁶³, 63, F₄, 63) (dual of [63, 0, 64]-code or 63-arc in PG(62,4)), using
  - complete OA / dual of code with only one code word [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(4¹⁷¹, 90, F₄, 2, 116) (dual of [(90, 2), 9, 117]-NRT-code)	[i]		OOA Folding
2	Linear OOA(4¹⁷¹, 60, F₄, 3, 116) (dual of [(60, 3), 9, 117]-NRT-code)	[i]		OOA Folding