A study of quantum error-correcting codes derived from platonic tilings
نویسندگان
چکیده
iii
منابع مشابه
Constacyclic Codes over Group Ring (Zq[v])/G
Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...
متن کاملOne-point Goppa Codes on Some Genus 3 Curves with Applications in Quantum Error-Correcting Codes
We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation yl = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x3 +x and Picard curves given by the equations y3 = x4-x and y3 = x4 -1. As a result, we obtain exact value of min...
متن کاملGood Families of Quantum Low - Density Parity - Check Codes and a Geometric Framework for the Amplitude - Damping Channel
Classical low-density parity-check (LDPC) codes were first introduced by Robert Gallager in the 1960's and have reemerged as one of the most influential coding schemes. We present new families of quantum low-density parity-check error-correcting codes derived from regular tessellations of Platonic 2-manifolds and from embeddings of the Lubotzky-Phillips-Sarnak Ramanujan graphs. These families o...
متن کاملThe partial order of perfect codes associated to a perfect code
It is clarified whether or not “full rank perfect 1-error correcting binary codes act like primes in the family of all perfect 1-error correcting binary codes”. Thereby the well known connection between perfect 1-error correcting binary codes and tilings will be discussed and used.
متن کاملStabilizer codes from modified symplectic form
Stabilizer codes form an important class of quantum error correcting codes[10, 2, 5] which have an elegant theory, efficient error detection, and many known examples. Constructing stabilizer codes of length n is equivalent to constructing subspaces of Fp ×Fp which are isotropic under the symplectic bilinear form defined by ⟨(a,b), (c,d)⟩ = aTd − bTc [10, 12, 1]. As a result, many, but not all, ...
متن کامل