MinT - Information on Result #1013210

Information on Result #1013210

Linear OOA(5¹⁰⁰, 651071, F₅, 3, 13) (dual of [(651071, 3), 1953113, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5⁹, 27, F₅, 3, 6) (dual of [(27, 3), 72, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (3, 9, 27)-net over F₅, using
  - linear code embedding found in a computer search [i]
linear OOA(5⁹¹, 651044, F₅, 3, 13) (dual of [(651044, 3), 1953041, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(5⁹¹, 1953132, F₅, 13) (dual of [1953132, 1953041, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(5⁹¹, 1953134, F₅, 13) (dual of [1953134, 1953043, 14]-code), using
    - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
      1. linear OA(5⁹¹, 1953125, F₅, 13) (dual of [1953125, 1953034, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 1953124Â = 5⁹âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. linear OA(5⁸², 1953125, F₅, 12) (dual of [1953125, 1953043, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 1953124Â = 5⁹âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      3. linear OA(5⁰, 9, F₅, 0) (dual of [9, 9, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(5⁰, s, F₅, 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(5¹⁰⁰, 325535, F₅, 15, 13) (dual of [(325535, 15), 4882925, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row