IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 45, NO. 6, SEPTEMBER 1999 2209

Correction

Correction to “New Double-ByteError-Correcting Codes for Memory Systems”

Gui-Liang Feng,Senior Member, IEEE,Xin-Wen Wu, and T. R. N. Rao,Fellow, IEEE

In the above paper,1 we constructed some classes of double-byteerror-correcting codes over GF(2i), which reduce the previouslyknown redundancy record. However, there are some flaws in theproofs of Theorems 3.3 and 3.4. In those proofs, we need to prove

(cq + a) cq + c 6= 0

Manuscript received October 13, 1998; revised February 22, 1999.G.-L. Feng and T. R. N. Rao are with the Center for Advanced Computer

Studies, University of Southwestern Louisiana, Lafayette, LA 70504 USA.X.-W. Wu is with the Institute of Mathematics, Chinese Academy of

Sciences, Beijing, 100080, China, and the Center for Advanced ComputerStudies, University of Southwestern Louisiana, Lafayette, LA 70504 USA.

Communicated by A. M. Barg, Associate Editor for Coding Theory.Publisher Item Identifier S 0018-9448(99)06030-7.1G. L. Feng, X. W. Wu, and T. R. N. Rao, “New double-byte error-

correcting codes for memory systems,”IEEE Trans. Inform. Theory, vol. 44,pp. 1152–1163, May 1998.

where c is some element in GF(qm), and a is in GF(q). Theinequalitycq + a 6= 0 was proved in those proofs. Whenm is odd,i.e., m = 3; 5; 7; � � � ; it can be shown thatcq + c 6= 0. However,whenm is even,cq + c may be zero. In the proofs of Theorems 3.3and 3.4, we failed to consider the case of evenm. Dr. C. L. Chenfirst found the flaws and gave two counter examples [1].

Construction 3.3 and Theorem 3.3 should be revised to the case ofm = 5, the construction and proof are similar to the original ones.Construction 3.4 and Theorem 3.4 should be restricted to the caseof m being odd. In summary, the paper has constructions for a classof double-byte error-correcting codes over GF(2i), with parameters:n = q

m; r � 2m + dm

3e + 1, for m odd (Theorem 3.4), and for

m a multiple of 3 (Theorem 5.1). In these cases, the constructionsreduce the redundance of Dummer forq even by one symbol. Andthe redundancy takes the same form as the redundancy of Dumerfor q odd.

REFERENCES

[1] C. L. Chen, “On double-byte error-correcting codes,” private commu-nication.

0018–9448/99$10.00 1999 IEEE