MinT - Information on Result #1164639

Information on Result #1164639

Linear OOA(2²⁰⁵, 2796201, F₂, 8, 12) (dual of [(2796201, 8), 22369403, 13]-NRT-code), using OOA stacking with additional row based on linear OOA(2²⁰⁵, 2796202, F₂, 6, 12) (dual of [(2796202, 6), 16777007, 13]-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(2¹⁴¹, 1398101, F₂, 6, 12) (dual of [(1398101, 6), 8388465, 13]-NRT-code), using
  - OOA 2-folding [i] based on linear OOA(2¹⁴¹, 2796202, F₂, 3, 12) (dual of [(2796202, 3), 8388465, 13]-NRT-code), using
    - 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹³⁸, 2796201, F₂, 3, 12) (dual of [(2796201, 3), 8388465, 13]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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		This result only	Method
1	Linear OOA(2²⁰⁷, 2796201, F₂, 8, 12) (dual of [(2796201, 8), 22369401, 13]-NRT-code)	[i]		OOA Duplication