MinT - Information on Result #1070215

Information on Result #1070215

Linear OOA(128⁶⁶, 4194301, F₁₂₈, 4, 12) (dual of [(4194301, 4), 16777138, 13]-NRT-code), using OOA 2-folding based on linear OOA(128⁶⁶, 8388602, F₁₂₈, 2, 12) (dual of [(8388602, 2), 16777138, 13]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(128²¹, 4194301, F₁₂₈, 2, 6) (dual of [(4194301, 2), 8388581, 7]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(128²¹, 8388602, F₁₂₈, 6) (dual of [8388602, 8388581, 7]-code), using
    - discarding factors / shortening the dual code based on linear OA(128²¹, large, F₁₂₈, 6) (dual of [large, large−21, 7]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 17895697Â | 128⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
2. linear OOA(128⁴⁵, 4194301, F₁₂₈, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(128⁴⁵, 8388602, F₁₂₈, 12) (dual of [8388602, 8388557, 13]-code), using
    - discarding factors / shortening the dual code based on linear OA(128⁴⁵, large, F₁₂₈, 12) (dual of [large, large−45, 13]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 9256395Â | 128⁴âˆ’1, defining interval IÂ =Â [0,11], 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(128⁶⁷, 4194301, F₁₂₈, 4, 12) (dual of [(4194301, 4), 16777137, 13]-NRT-code)	[i]		OOA Duplication