MinT - Information on Result #901912

Information on Result #901912

Linear OOA(32³², 579, F₃₂, 2, 12) (dual of [(579, 2), 1126, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32⁹, 66, F₃₂, 2, 6) (dual of [(66, 2), 123, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(32³, 33, F₃₂, 2, 3) (dual of [(33, 2), 63, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;63,32) [i]
  2. linear OOA(32⁶, 33, F₃₂, 2, 6) (dual of [(33, 2), 60, 7]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;60,32) [i]
linear OOA(32²³, 513, F₃₂, 2, 12) (dual of [(513, 2), 1003, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32²³, 1026, F₃₂, 12) (dual of [1026, 1003, 13]-code), using
  - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
    1. linear OA(32²³, 1024, F₃₂, 12) (dual of [1024, 1001, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
    2. linear OA(32²¹, 1024, F₃₂, 11) (dual of [1024, 1003, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
    3. linear OA(32⁰, 2, F₃₂, 0) (dual of [2, 2, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 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.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(32³², 192, F₃₂, 14, 12) (dual of [(192, 14), 2656, 13]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row