MinT - Information on Result #1301477

Information on Result #1301477

Linear OA(5⁷², 78162, F₅, 12) (dual of [78162, 78090, 13]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(5⁷¹, 78160, F₅, 12) (dual of [78160, 78089, 13]-code), using
- constructionÂ X applied to C_e(11) âŠ‚ C_e(6) [i] based on
  1. linear OA(5⁶⁴, 78125, F₅, 12) (dual of [78125, 78061, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 78124Â = 5⁷âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
  2. linear OA(5³⁶, 78125, F₅, 7) (dual of [78125, 78089, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 78124Â = 5⁷âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
  3. linear OA(5⁷, 35, F₅, 4) (dual of [35, 28, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(5⁷, 44, F₅, 4) (dual of [44, 37, 5]-code), using
      - codes constructed by inverting constructionÂ Y₁ [i]
linear OA(5⁷¹, 78161, F₅, 11) (dual of [78161, 78090, 12]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 5⁷¹Â > V_b^sâˆ’1(kâˆ’1)Â = 2 457232 375386 571927 384568 086699 247212 011322 051265 [i]
linear OA(5⁰, 1, F₅, 0) (dual of [1, 1, 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: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(5⁷², 78162, F₅, 2, 12) (dual of [(78162, 2), 156252, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(5⁷², 78162, F₅, 3, 12) (dual of [(78162, 3), 234414, 13]-NRT-code)	[i]
3	Digital (60, 72, 78162)-net over F₅	[i]
4	Linear OOA(5⁷², 39081, F₅, 2, 12) (dual of [(39081, 2), 78090, 13]-NRT-code)	[i]	OOA Folding