MinT - Information on Result #1543173

Information on Result #1543173

Linear OOA(4²²², 3164676, F₄, 3, 25) (dual of [(3164676, 3), 9493806, 26]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4²²², 3164676, F₄, 2, 25) (dual of [(3164676, 2), 6329130, 26]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4²²², 4194303, F₄, 2, 25) (dual of [(4194303, 2), 8388384, 26]-NRT-code), using
- 4¹ times duplication [i] based on linear OOA(4²²¹, 4194303, F₄, 2, 25) (dual of [(4194303, 2), 8388385, 26]-NRT-code), using
  - 2 times NRT-code embedding in larger space [i] based on linear OOA(4²¹⁷, 4194301, F₄, 2, 25) (dual of [(4194301, 2), 8388385, 26]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(4²¹⁷, 8388602, F₄, 25) (dual of [8388602, 8388385, 26]-code), using
      - discarding factors / shortening the dual code based on linear OA(4²¹⁷, large, F₄, 25) (dual of [large, large−217, 26]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 4²⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]

Mode: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m 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(4²²², 791168, F₄, 27, 25) (dual of [(791168, 27), 21361314, 26]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row