MinT - Information on Result #641085

Information on Result #641085

Linear OA(4¹³⁴, 141, F₄, 93) (dual of [141, 7, 94]-code), using juxtaposition based on

linear OA(4⁵⁵, 62, F₄, 41) (dual of [62, 7, 42]-code), using
- discarding factors / shortening the dual code based on 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]
linear OA(4⁷², 79, F₄, 51) (dual of [79, 7, 52]-code), using
- discarding factors / shortening the dual code based on linear OA(4⁷², 80, F₄, 51) (dual of [80, 8, 52]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(16¹², 16, F₁₆, 12) (dual of [16, 4, 13]-code or 16-arc in PG(11,16)), using
      - Reedâ€“Solomon code RS(4,16) [i]
    2. linear OA(4³, 5, F₄, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,4) or 5-cap in PG(2,4)), using
      - extended Reedâ€“Solomon code RS_e(2,4) [i]
      - Simplex code S(2,4) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(4¹⁹⁷, 204, F₄, 136) (dual of [204, 7, 137]-code)	[i]		Juxtaposition