Cyclic constant dimension subspace codes via the sum of Sidon spaces

作者：Li, Yun; Liu, Hongwei^*

来源：Designs, Codes, and Cryptography, 2022.

DOI：10.1007/s10623-022-01146-9

• Cyclic subspace codes
• Constant dimension codes
• Sum of Sidon spaces
• Network coding

Subspace codes are of great use in noncoherent linear network coding (Katti et al in ACM SIGCOMM Comput Commun Rev 38(4):401-412, 2008; Kotter and Kschischang in IEEE Trans Inform Theory 54(8):3579-3591, 2008; Silva et al. in IEEE Trans Inform Theory 54(9):3951-3967, 2008). As a particular subclass of subspace codes, cyclic constant dimension subspace codes can be encoded and decoded more efficiently. There is an increased interest in constructing cyclic constant dimension subspace codes whose sizes and minimum distances are as large as possible. Roth et al. (IEEE Trans Inform Theory 64(6):4412-4422, 2017) constructed several cyclic constant dimension subspace codes using Sidon spaces. In this paper, we present a criterion which can be used to determine whether or not the sum of some distinct Sidon spaces is again a Sidon space. Based on this result, we obtain cyclic constant dimension subspace codes via the sum of several Sidon spaces. Our results generalize some results in Niu et al. (Discret Math 343(5):111788, 2020) and Roth et al. (IEEE Trans Inform Theory 64(6):4412-4422, 2017).