MinT - Information on Result #2520028

Information on Result #2520028

Linear OOA(32¹⁰⁹, large, F₃₂, 2, 14), using 6 times NRT-code embedding in larger space based on linear OOA(32⁹⁷, 8388602, F₃₂, 2, 14) (dual of [(8388602, 2), 16777107, 15]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(32³¹, 4194301, F₃₂, 2, 7) (dual of [(4194301, 2), 8388571, 8]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(32³¹, 8388602, F₃₂, 7) (dual of [8388602, 8388571, 8]-code), using
    - discarding factors / shortening the dual code based on linear OA(32³¹, large, F₃₂, 7) (dual of [large, large−31, 8]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 33554433Â | 32¹⁰âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
2. linear OOA(32⁶⁶, 4194301, F₃₂, 2, 14) (dual of [(4194301, 2), 8388536, 15]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(32⁶⁶, 8388602, F₃₂, 14) (dual of [8388602, 8388536, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(32⁶⁶, large, F₃₂, 14) (dual of [large, large−66, 15]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 33554431Â = 32⁵âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and t, 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(32¹¹⁰, large, F₃₂, 2, 14)	[i]		OOA Duplication