MinT - Information on Result #2528678

Information on Result #2528678

OOA(128⁶⁹, large, S₁₂₈, 2, 13), using 4 times NRT-code embedding in larger space based on OOA(128⁶¹, 8388602, S₁₂₈, 2, 13), using

discarding parts of the base [i] based on linear OOA(256⁵³, 8388602, F₂₅₆, 2, 13) (dual of [(8388602, 2), 16777151, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256¹⁶, 4194301, F₂₅₆, 2, 6) (dual of [(4194301, 2), 8388586, 7]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(256¹⁶, 8388602, F₂₅₆, 6) (dual of [8388602, 8388586, 7]-code), using
      - discarding factors / shortening the dual code based on linear OA(256¹⁶, large, F₂₅₆, 6) (dual of [large, large−16, 7]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
  2. linear OOA(256³⁷, 4194301, F₂₅₆, 2, 13) (dual of [(4194301, 2), 8388565, 14]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(256³⁷, 8388602, F₂₅₆, 13) (dual of [8388602, 8388565, 14]-code), using
      - discarding factors / shortening the dual code based on linear OA(256³⁷, large, F₂₅₆, 13) (dual of [large, large−37, 14]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]

Mode: Constructive.

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	OOA(128⁷⁰, large, S₁₂₈, 2, 13)	[i]		OOA Duplication