MinT - Information on Result #1164798

Information on Result #1164798

Linear OOA(2²⁰⁶, 2796201, F₂, 8, 13) (dual of [(2796201, 8), 22369402, 14]-NRT-code), using OOA stacking with additional row based on linear OOA(2²⁰⁶, 2796202, F₂, 6, 13) (dual of [(2796202, 6), 16777006, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁶⁴, 2097149, F₂, 6, 6) (dual of [(2097149, 6), 12582830, 7]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(2⁶⁴, 2097150, F₂, 3, 6) (dual of [(2097150, 3), 6291386, 7]-NRT-code), using
    - 1 step truncation [i] based on linear OOA(2⁶⁵, 2097151, F₂, 3, 7) (dual of [(2097151, 3), 6291388, 8]-NRT-code), using
      - OOAs constructed from BCH codes [i]
2. linear OOA(2¹⁴², 1398101, F₂, 6, 13) (dual of [(1398101, 6), 8388464, 14]-NRT-code), using
  - OOA 2-folding [i] based on linear OOA(2¹⁴², 2796202, F₂, 3, 13) (dual of [(2796202, 3), 8388464, 14]-NRT-code), using
    - 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹³⁹, 2796201, F₂, 3, 13) (dual of [(2796201, 3), 8388464, 14]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(2¹³⁹, large, F₂, 13) (dual of [large, large−139, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Constructive and 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		Method
1	Linear OOA(2²⁰⁶, 2796201, F₂, 8, 12) (dual of [(2796201, 8), 22369402, 13]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²⁰⁷, 2796201, F₂, 8, 13) (dual of [(2796201, 8), 22369401, 14]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁰⁸, 2796201, F₂, 8, 13) (dual of [(2796201, 8), 22369400, 14]-NRT-code)	[i]	OOA Duplication