MinT - Information on Result #1145032

Information on Result #1145032

Linear OOA(256⁴⁷, 1398615, F₂₅₆, 6, 13) (dual of [(1398615, 6), 8391643, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(256¹⁰, 515, F₂₅₆, 6, 6) (dual of [(515, 6), 3080, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(256¹⁰, 515, F₂₅₆, 5, 6) (dual of [(515, 5), 2565, 7]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(256³, 257, F₂₅₆, 5, 3) (dual of [(257, 5), 1282, 4]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(5;1282,256) [i]
    2. linear OOA(256⁷, 258, F₂₅₆, 5, 6) (dual of [(258, 5), 1283, 7]-NRT-code), using
      - extracting embedded OOA [i] based on digital (1, 7, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
linear OOA(256³⁷, 1398100, F₂₅₆, 6, 13) (dual of [(1398100, 6), 8388563, 14]-NRT-code), using
- OOA 6-folding [i] based on linear OA(256³⁷, 8388600, F₂₅₆, 13) (dual of [8388600, 8388563, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(256³⁷, large, F₂₅₆, 13) (dual of [large, large−37, 14]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(256⁴⁷, 1398614, F₂₅₆, 18, 13) (dual of [(1398614, 18), 25175005, 14]-NRT-code)	[i]		OOA Stacking with Additional Row