2022/12/26 by Debnath, Indibar, Singh, Ashutosh, Prakash, Om +1
#94B05 #94B15 #94B35 #94B60 #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2212.13169
Let ℤp be the ring of integers modulo a prime number p where p-1 is a quadratic residue modulo p. This paper presents the study of constacyclic codes over chain rings R=(ℤp[u])/(⟨ u2⟩) and S=(ℤp[u])/(⟨ u3⟩). We also study additive constacyclic codes over RS and ℤpRS using the generator polynomials over the rings R and S, respectively. Further, by defining Gray maps on R, S and ℤpRS, we obtain some results on the Gray images of additive codes. Then we give the weight enumeration and MacWilliams identities corresponding to the additive codes over ℤpRS. Finally, as an application of the obtained codes, we give quantum codes using the CSS construction.