MinT - Information on Result #1083940

Information on Result #1083940

Linear OOA(256⁶⁸, 2113791, F₂₅₆, 4, 17) (dual of [(2113791, 4), 8455096, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(256¹⁹, 16641, F₂₅₆, 4, 8) (dual of [(16641, 4), 66545, 9]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256⁴, 257, F₂₅₆, 4, 4) (dual of [(257, 4), 1024, 5]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(4;1024,256) [i]
  2. linear OOA(256¹⁵, 16384, F₂₅₆, 4, 8) (dual of [(16384, 4), 65521, 9]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(256¹⁵, 65536, F₂₅₆, 8) (dual of [65536, 65521, 9]-code), using
      - an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
linear OOA(256⁴⁹, 2097150, F₂₅₆, 4, 17) (dual of [(2097150, 4), 8388551, 18]-NRT-code), using
- OOA 4-folding [i] based on linear OA(256⁴⁹, 8388600, F₂₅₆, 17) (dual of [8388600, 8388551, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(256⁴⁹, large, F₂₅₆, 17) (dual of [large, large−49, 18]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(256⁶⁸, 1056895, F₂₅₆, 20, 17) (dual of [(1056895, 20), 21137832, 18]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row