MinT - Information on Result #896471

Information on Result #896471

Linear OOA(8³¹, 1048588, F₈, 2, 5) (dual of [(1048588, 2), 2097145, 6]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8², 9, F₈, 2, 2) (dual of [(9, 2), 16, 3]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;16,8) [i]
linear OOA(8²⁹, 1048579, F₈, 2, 5) (dual of [(1048579, 2), 2097129, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8²⁹, 2097158, F₈, 5) (dual of [2097158, 2097129, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(8²⁹, 2097159, F₈, 5) (dual of [2097159, 2097130, 6]-code), using
    - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
      1. linear OA(8²⁹, 2097152, F₈, 5) (dual of [2097152, 2097123, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      2. linear OA(8²², 2097152, F₈, 4) (dual of [2097152, 2097130, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      3. linear OA(8⁰, 7, F₈, 0) (dual of [7, 7, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8³¹, 1048587, F₈, 3, 5) (dual of [(1048587, 3), 3145730, 6]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(8³¹, 1048587, F₈, 6, 5) (dual of [(1048587, 6), 6291491, 6]-NRT-code)	[i]		OOA Stacking with Additional Row