MinT - Information on Result #1014733

Information on Result #1014733

Linear OOA(8¹⁵⁸, 5592562, F₈, 3, 18) (dual of [(5592562, 3), 16777528, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8²⁰, 160, F₈, 3, 9) (dual of [(160, 3), 460, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (11, 20, 160)-net over F₈, using
  - trace code for nets [i] based on digital (1, 10, 80)-net over F₆₄, using
    - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
        a function field by SÃ©mirat [i]
linear OOA(8¹³⁸, 5592402, F₈, 3, 18) (dual of [(5592402, 3), 16777068, 19]-NRT-code), using
- trace code [i] based on linear OOA(64⁶⁹, 2796201, F₆₄, 3, 18) (dual of [(2796201, 3), 8388534, 19]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(64⁶⁹, large, F₆₄, 18) (dual of [large, large−69, 19]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8¹⁵⁹, 5592562, F₈, 3, 18) (dual of [(5592562, 3), 16777527, 19]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(8¹⁵⁸, 1864187, F₈, 21, 18) (dual of [(1864187, 21), 39147769, 19]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row