I'm currently studying this paper:
''Modular and p-adic Cyclic Codes'', A. Robert Calderbank, N. J. A. Sloane, published 1995 in Designs, Codes, Cryptography DOI:10.1007/BF01390768
but am having a hard time understanding this since I have no background on cyclic codes, lifting, etc.
Do you know of any resources/books that I could read in order to have enough background to understand this paper? Thank you!
You could try a newer text book: "Coding Theory - A First Course" by San Ling and C. Xing, 2004. But the classical texts by J. van Lint, and J. MacWilliams and N. Sloane are still one of the best out there.