MinT - Information on Result #1071479

Information on Result #1071479

Linear OOA(256⁵⁰, 4194301, F₂₅₆, 4, 12) (dual of [(4194301, 4), 16777154, 13]-NRT-code), using OOA 2-folding based on linear OOA(256⁵⁰, 8388602, F₂₅₆, 2, 12) (dual of [(8388602, 2), 16777154, 13]-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(256³⁴, 4194301, F₂₅₆, 2, 12) (dual of [(4194301, 2), 8388568, 13]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(256³⁴, 8388602, F₂₅₆, 12) (dual of [8388602, 8388568, 13]-code), using
    - discarding factors / shortening the dual code based on linear OA(256³⁴, large, F₂₅₆, 12) (dual of [large, large−34, 13]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’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(256⁵¹, 4194301, F₂₅₆, 4, 12) (dual of [(4194301, 4), 16777153, 13]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(256⁶⁶, 6990502, F₂₅₆, 4, 12) (dual of [(6990502, 4), 27961942, 13]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs