MinT - Information on Result #663432

Information on Result #663432

Linear OA(8²³, 64528, F₈, 5) (dual of [64528, 64505, 6]-code), using generalized (u,Â u+v)-construction based on

linear OA(8⁰, 8066, F₈, 0) (dual of [8066, 8066, 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]
linear OA(8⁰, 8066, F₈, 0) (dual of [8066, 8066, 1]-code) (see above)
linear OA(8⁰, 8066, F₈, 0) (dual of [8066, 8066, 1]-code) (see above)
linear OA(8¹, 8066, F₈, 1) (dual of [8066, 8065, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(8¹, s, F₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
  - parity-check code [i]
linear OA(8¹, 8066, F₈, 1) (dual of [8066, 8065, 2]-code) (see above)
linear OA(8¹, 8066, F₈, 1) (dual of [8066, 8065, 2]-code) (see above)
linear OA(8⁶, 8066, F₈, 2) (dual of [8066, 8060, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(8⁶, 32768, F₈, 2) (dual of [32768, 32762, 3]-code), using
  - an extension C_e(1) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 2 [i]
linear OA(8¹⁴, 8066, F₈, 5) (dual of [8066, 8052, 6]-code), using
- trace code [i] based on linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 6]-code), using
  - a code by Danev and Olsson [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(8²³, 64528, F₈, 2, 5) (dual of [(64528, 2), 129033, 6]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(8²³, 64528, F₈, 3, 5) (dual of [(64528, 3), 193561, 6]-NRT-code)	[i]
3	Digital (18, 23, 64528)-net over F₈	[i]
4	Linear OOA(8²³, 32264, F₈, 2, 5) (dual of [(32264, 2), 64505, 6]-NRT-code)	[i]	OOA Folding