MinT - Information on Result #683995

Information on Result #683995

Linear OA(5¹²¹, 148, F₅, 71) (dual of [148, 27, 72]-code), using constructionÂ X applied to C([0,36]) âŠ‚ C([0,31]) based on

linear OA(5¹¹¹, 126, F₅, 73) (dual of [126, 15, 74]-code), using the expurgated narrow-sense BCH-code C(I) with length 126Â | 5⁶âˆ’1, defining interval IÂ =Â [0,36], and minimum distance dÂ â‰¥ |{−36,−35,…,36}|+1Â =Â 74 (BCH-bound) [i]
linear OA(5⁹⁹, 126, F₅, 63) (dual of [126, 27, 64]-code), using the expurgated narrow-sense BCH-code C(I) with length 126Â | 5⁶âˆ’1, defining interval IÂ =Â [0,31], and minimum distance dÂ â‰¥ |{−31,−30,…,31}|+1Â =Â 64 (BCH-bound) [i]
linear OA(5¹⁰, 22, F₅, 7) (dual of [22, 12, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(5¹⁰, 24, F₅, 7) (dual of [24, 14, 8]-code), using
  - the primitive expurgated narrow-sense BCH-code C(I) with length 24Â = 5²âˆ’1, defining interval IÂ =Â [0,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OA(5¹²¹, 148, F₅, 70) (dual of [148, 27, 71]-code)	[i]	Strength Reduction
2	Linear OA(5¹²¹, 148, F₅, 69) (dual of [148, 27, 70]-code)	[i]
3	Linear OA(5¹²¹, 148, F₅, 68) (dual of [148, 27, 69]-code)	[i]
4	Linear OA(5¹²¹, 148, F₅, 67) (dual of [148, 27, 68]-code)	[i]
5	Linear OA(5¹²⁵, 152, F₅, 71) (dual of [152, 27, 72]-code)	[i]	Code Embedding in Larger Space
6	Linear OA(5¹²⁰, 147, F₅, 70) (dual of [147, 27, 71]-code)	[i]	Truncation
7	Linear OA(5¹¹⁹, 146, F₅, 69) (dual of [146, 27, 70]-code)	[i]
8	Linear OA(5¹¹⁴, 141, F₅, 64) (dual of [141, 27, 65]-code)	[i]
9	Linear OA(5¹²³, 151, F₅, 71) (dual of [151, 28, 72]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
10	Linear OOA(5¹²¹, 74, F₅, 2, 71) (dual of [(74, 2), 27, 72]-NRT-code)	[i]	OOA Folding
11	Linear OOA(5¹²¹, 49, F₅, 3, 71) (dual of [(49, 3), 26, 72]-NRT-code)	[i]	OOA Folding