MinT - Information on Result #1422422

Information on Result #1422422

Linear OOA(4¹²⁴, 54300, F₄, 2, 19) (dual of [(54300, 2), 108476, 20]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4¹²⁴, 54300, F₄, 19) (dual of [54300, 54176, 20]-code), using

discarding factors / shortening the dual code based on linear OA(4¹²⁴, 65552, F₄, 19) (dual of [65552, 65428, 20]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(4¹¹, 15, F₄, 9) (dual of [15, 4, 10]-code), using
    - 2 times truncation [i] based on linear OA(4¹³, 17, F₄, 11) (dual of [17, 4, 12]-code), using
      - projective code from ovoid in PG(3,Â 4) [i]
  2. linear OA(4¹¹³, 65537, F₄, 19) (dual of [65537, 65424, 20]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 65537Â | 4¹⁶âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]

Mode: 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4¹²⁴, 27150, F₄, 3, 19) (dual of [(27150, 3), 81326, 20]-NRT-code)	[i]		OOA Folding