MinT - Information on Result #2519869

Information on Result #2519869

Linear OOA(32⁷⁵, large, F₃₂, 2, 10), using 4 times NRT-code embedding in larger space based on linear OOA(32⁶⁷, 8388602, F₃₂, 2, 10) (dual of [(8388602, 2), 16777137, 11]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(32²¹, 4194301, F₃₂, 2, 5) (dual of [(4194301, 2), 8388581, 6]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(32²¹, 8388602, F₃₂, 5) (dual of [8388602, 8388581, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(32²¹, large, F₃₂, 5) (dual of [large, large−21, 6]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 33554433Â | 32¹⁰âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
2. linear OOA(32⁴⁶, 4194301, F₃₂, 2, 10) (dual of [(4194301, 2), 8388556, 11]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(32⁴⁶, 8388602, F₃₂, 10) (dual of [8388602, 8388556, 11]-code), using
    - discarding factors / shortening the dual code based on linear OA(32⁴⁶, large, F₃₂, 10) (dual of [large, large−46, 11]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 33554431Â = 32⁵âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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(32⁷⁶, large, F₃₂, 2, 10)	[i]		OOA Duplication