A Construction of Multisender Authentication Codes with Sequential Model from Symplectic Geometry over Finite Fields

Table 1

(𝑛>𝑟/2,𝑛^′−𝑛>𝜈−𝑟).

Constructions	[19]	Size relation	Ours
The number of senders	𝑛	=	𝑛
The number of attackers	𝑙,1≤𝑙<𝑛	=	𝑙,1≤𝑙<𝑛
The parameters of codes
|𝑆|	𝑁(2(𝑟−𝑛),𝑟−𝑛;2(𝜈−𝑛))	=	𝑁(2(𝑟−𝑛),𝑟−𝑛;2(𝜈−𝑛))
𝐸𝑖	𝑞^2(𝜈−𝑛)	=	𝑞^2(𝜈−𝑛)
𝐸𝑅	𝑞^2𝑛′(𝜈−𝑛′)	>	𝑞^2𝑛(𝜈−𝑛)
|𝑇|	𝑁(2(𝑟−𝑛),𝑟−𝑛;2(𝜈−𝑛))𝑞^2𝑛′(𝜈−𝑟−𝑛′+𝑛)	<	𝑁(2(𝑟−𝑛),𝑟−𝑛;2(𝜈−𝑛))𝑞^2𝑛(𝜈−𝑟)
The probabilities of deceptions
𝑃𝐼(𝐿)	1𝑞^2(𝑛′−𝑙)(𝜈+𝑛−𝑛′−𝑟)−(𝑛′−𝑛)(𝑛−𝑙)	>	1𝑞^2(𝑛−𝑙)(𝜈−𝑟)
𝑃𝑆(𝐿)	1𝑞^(𝑛′−𝑙)(2𝑛−2𝑛′+1)+(𝑛′−𝑛)(𝑛−𝑙)	>	1𝑞^𝑛−𝑙