MinT - Information on Result #1071527

Information on Result #1071527

Linear OOA(256⁵⁹, 4194301, F₂₅₆, 4, 14) (dual of [(4194301, 4), 16777145, 15]-NRT-code), using OOA 2-folding based on linear OOA(256⁵⁹, 8388602, F₂₅₆, 2, 14) (dual of [(8388602, 2), 16777145, 15]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(256¹⁹, 4194301, F₂₅₆, 2, 7) (dual of [(4194301, 2), 8388583, 8]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(256¹⁹, 8388602, F₂₅₆, 7) (dual of [8388602, 8388583, 8]-code), using
    - discarding factors / shortening the dual code based on linear OA(256¹⁹, large, F₂₅₆, 7) (dual of [large, large−19, 8]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
2. linear OOA(256⁴⁰, 4194301, F₂₅₆, 2, 14) (dual of [(4194301, 2), 8388562, 15]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(256⁴⁰, 8388602, F₂₅₆, 14) (dual of [8388602, 8388562, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(256⁴⁰, large, F₂₅₆, 14) (dual of [large, large−40, 15]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’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 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(256⁶⁰, 4194301, F₂₅₆, 4, 14) (dual of [(4194301, 4), 16777144, 15]-NRT-code)	[i]		OOA Duplication