2025/09/23 by Wang, Gang, Xu, Ming, Gao, You
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2509.18704
In this paper, two new constructions of Sidon spaces are given by tactfully adding new parameters and flexibly varying the number of parameters. Under the parameters n= (2r+1)k, r ≥2 and p0=max \i∈ ℕ+: \lfloor (r)/(i)\rfloor>\lfloor (r)/(i+1) \rfloor \, the first construction produces a cyclic CDC in Gq(n, k) with minimum distance 2k-2 and size \frac((r+∑i=2p0(\lfloor (r)/(i)\rfloor-\lfloor (r)/(i+1) \rfloor))(qk-1)(q-1)+r)(qk-1)r-1(qn-1)q-1. Given parameters n=2rk,r≥ 2 and if r=2, p0=1, otherwise, p0=max\ i∈ ℕ+: \lceil(r)/(i)\rceil-1>\lfloor (r)/(i+1) \rfloor \, a cyclic CDC in Gq(n, k) with minimum distance 2k-2 and size \frac((r-1+∑i=2p0(\lceil (r)/(i)\rceil-\lfloor (r)/(i+1) \rfloor-1))(qk-1)(q-1)+r-1)(qk-1)r-2\lfloor (qk-2)/(2)\rfloor(qn-1)q-1 is produced by the second construction. The sizes of our cyclic CDCs are larger than the best known results. In particular, in the case of n=4k, when k goes to infinity, the ratio between the size of our cyclic CDC and the Sphere-packing bound (Johnson bound) is approximately equal to (1)/(2). Moreover, for a prime power q and positive integers k,s with 1≤ s< k-1, a cyclic CDC in Gq(N, k) of size e(qN-1)/(q-1) and minimum distance ≥ 2k-2s is provided by subspace polynomials, where N,e are positive integers. Our construction generalizes previous results and, under certain parameters, provides cyclic CDCs with larger sizes or more admissible values of N than constructions based on trinomials.