MinT - Information on Result #905673

Information on Result #905673

Linear OOA(256⁵⁴, 4194816, F₂₅₆, 2, 15) (dual of [(4194816, 2), 8389578, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(256¹¹, 515, F₂₅₆, 2, 7) (dual of [(515, 2), 1019, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256³, 257, F₂₅₆, 2, 3) (dual of [(257, 2), 511, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;511,256) [i]
  2. linear OOA(256⁸, 258, F₂₅₆, 2, 7) (dual of [(258, 2), 508, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 8, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
linear OOA(256⁴³, 4194301, F₂₅₆, 2, 15) (dual of [(4194301, 2), 8388559, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(256⁴³, 8388602, F₂₅₆, 15) (dual of [8388602, 8388559, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(256⁴³, large, F₂₅₆, 15) (dual of [large, large−43, 16]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	OOA(128⁶², 4194816, S₁₂₈, 2, 15)	[i]		Discarding Parts of the Base for OOAs
2	Linear OOA(256⁵⁴, 2097408, F₂₅₆, 4, 15) (dual of [(2097408, 4), 8389578, 16]-NRT-code)	[i]		OOA Folding