Iranian Mathematical Society Journal of the Iranian Mathematical Society 2717-1612 6 1 2025 01 01 $\epsilon$-infinite frames for $k$-erasures 91 105 223502 10.30504/jims.2025.452123.1172 EN M. A. Hasankhani Fard Department of Mathematics, Vali-e-Asr University of Rafsanjan‎, ‎P.O. Box 546, Rafsanjan‎, ‎Iran. 0000-0001-5734-1576 A. Nazari Department of Pure Mathematics‎, ‎Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman‎, ‎P.O. Box 76169-14111, Kerman‎, ‎Iran. Journal Article 2024 04 12 Holmes and Paulsen studied finite frames from the viewpoint of coding theory‎. ‎In this paper, ‎for given $0<\epsilon\leq1$ and natural number $k$‎, ‎we introduce $\epsilon$-infinite frames for $k$-erasures in infinite-dimensional separable Hilbert space $\mathcal{H}$ from the of coding theory‎. ‎Additionally‎, ‎the perturbation and redundancy of $\epsilon$-infinite frames for $k$-erasures are studied‎. ‎Frames‎ ‎dual frames‎ ‎erasures‎ ‎redundancy‎ ‎perturbation https://jims.ims.ir/article_223502_03460814f8206532df96918b3192f597.pdf