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This paper is cited in the following contexts:
Nonbinary Quantum Stabilizer Codes - Ashikhmin, Knill (2000) (8 citations) (Correct)
....theory of binary quantum stabilizer codes is now well developed, nonbinary codes have been relatively ignored. A connection between classical codes over Zn and quantum codes is given in [11, 12] The connection is based on a stabilizer construction derived from so called nice error bases. Raines [16] obtained a number of results for p ary (p Bell Laboratories, Lucent Technologies, 600 Mountain Ave. Rm. 2C 180, Murray Hill, NJ 07974. y Los Alamos National Laboratory Group CIC 3, Mail Stop K987, Los Alamos, NM 87545. prime) quantum stabilizer codes generalizing the F 4 constructions ....
E. Rains, Nonbinary quantum codes, LANL eprint quant-ph/9703048.
Quantum Error Detection II: Bounds - Ashikhmin, Barg, Knill, Litsyn (2000) (1 citation) (Correct)
....being that once we look at q 2; it does not make much of a difference whether it is 4 or anything else, and that this is helpful in studying error detection of nonbinary classical codes on which we plan to report elsewhere. Moreover, the theory of quantum codes generalizes to larger q [8] [14], though the presentation is somewhat less systematic and the results more scattered than for binary quantum codes. Some further remarks on notation. Throughout the paper F = F 4 = f0; 1; 2 g: The Krawtchouk polynomial is given by K k (q; x) n X =0 ( Gamma1) x n Gamma ....
E. Rains, Nonbinary quantum codes, IEEE Trans. Inform. Theory, vol. 45, no. 6, pp. 1837--1832, 1999.
Clifford Codes - Klappenecker, Rötteler (Correct)
....refer to articles by Knill, La amme, and Viola [18] and by Zanardi [25] for more recent discussions of the general theory of quantum error control codes. b) The notion of detectable errors has been explicitly introduced in [17] in the form (1.6) The equivalent form (1. 4) has been used by Rains [19] in his de nition of minimum distance of a quantum 1.4. NICE ERROR BASES 7 code. Alternatively, one can de ne a detectable error by the orthogonality condition (1.7) as is shown by Lemma 1.1 and 1.2. Detectable errors have been studied in detail by Ashikhmin, Barg, Knill, and Litsyn in [2, 3] ....
E.M. Rains. Nonbinary quantum codes. IEEE Trans. Inform. Theory, 45:1827-1832, 1999.
Quantum Noise Control - Algebraic Methods - Knill (Correct)
....Theorem 13: G is solvable. Klappenecker Roetteler 2001 [14] Stabilizer Codes: Clifford code with # (irrep of H G) one dimensional. Gottesman 1996 [15] Klappenecker Roetteler 2001 [13] GF p 2n codes. Stabilizer Codes with G # GF p 2n . Calderbank al. 1996 [16] Rains 1997 [17] Ashikhmin Knill 2000 [18] 23 TOC Conclusion and Open Problems . Problem 7: What is the minimum size C(t, N) of the largest E detecting c code Thm. 6: C(t, N) # N t. Problem 10: What is the minimum size Q(t, N) of the largest E detecting q code Cor. 9: Q(t, N) # N (t(t 1) ....
E. R. Rains. Nonbinary quantum codes. quant-ph/9703048, 1997.
Quantum Error Detection II: Bounds - Ashikhmin, Barg, Knill, Litsyn (2000) (1 citation) (Correct)
....) the reasons being that once we look at , it does not make much of a difference whether it is or anything else, and that this is helpful in studying error detection of nonbinary classical codes on which we plan to report elsewhere. Moreover, the theory of quantum codes generalizes to larger [8] [14], though the presentation is somewhat less systematic and the results more scattered than for binary quantum codes. Some further remarks on notation. Throughout the paper . The Krawtchouk polynomial is given by (the implicit parameter the length of the code is usually clear from the ....
E. Rains, "Nonbinary quantum codes," IEEE Trans. Inform. Theory, vol. 45, pp. 1827--1832, Nov. 1999.
Quantum Error Correction Via Codes Over GF(4) - Calderbank, Rains, Shor, Sloane (1998) (27 citations) Self-citation (Rains) (Correct)
....codes (cf. Theorem 17) 58] and an analogous n=6 bound for classical singly even binary self dual codes [57] viii) The main construction in this paper (described in Section 2) can be generalized to primes greater than 2. Some preliminary work along these lines has been done in [2] 45] 46] [60]. ix) There are analogues of parts (a) c) of Theorem 6 for nonadditive codes. Parts (a) and (c) are trivial, while (b) now asserts that if a pure ( n; K; d) codes exists with n 2 then an ( n Gamma 1; 2K; d Gamma 1) code exists [59] x) How much of a restriction is it to use only ....
E. M. Rains, "Nonbinary quantum codes," LANL e-print quant-ph/9703048
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