Let p be an odd prime, s and m be positive integers. Cyclic codes of length 2psover Fpmare the ideals ((x-1)i(x+1)j), where 0 ≤ i, j ≤ ps, of the principal ideal ring Fpm[x]/(x2ps- 1). Using this structure, the symbol-pair distances of all cyclic codes of length 2psover Fpmare completely determined. In addition, we establish all MDS symbol-pair cyclic codes of length 2psover Fpm. Some MDS symbol-pair cyclic codes are better than all the known ones. Among others, we discuss possible applications to construct quantum MDS symbol-pair codes.

Let p be a prime, and λ be a nonzero element of the finite field Fpm. The λ-constacyclic codes of length psover Fpmare linearly ordered under set-theoretic inclusion, i.e., they are the ideals 〈(x - λ0)i〉, 0 ≤ i ≤ psof the chain ring [(Fpm[x])/((xps- λ))]. This structure is used to establish the symbol-pair distances of all such λ-constacyclic codes. Among others, all maximum distance separable symbol-pair constacyclic codes of length ps are obtained.

For any given positive integer m, a necessary and sufficient condition for the existence of Type-I m-adic constacyclic codes is given. Furthermore, for any given integer s, a necessary and sufficient condition for s to be a multiplier of a Type-I polyadic constacyclic code is given. As an application, some optimal codes from Type-I polyadic constacyclic codes, including generalized Reed-Solomon codes and alternant maximum distance separable codes, are constructed.

In SAR applications, the size of data can be quite large, and many data compression algorithms have been developed to reduce the storage requirements for SAR data. Previous research has been done on the compression of both amplitude and raw SAR data. However, the performance metrics used in these compression schemes are often visual-related metrics such as peak-signal-to-noise ratio (PSNR) or signal-to-quantization-noise ratio (SQNR). These metrics have been shown to provide misleading results for data with large dynamic range such as raw SAR data. The present research evaluates the performance of popular compression algorithms for raw SAR data in both SQNR and coherent change detection (CCD), which is superior in detecting subtle, man-made changes in the scene [1]. The results shows that higher SQNR does not lead to better CCD. This finding determines that the popular compression methods currently being used are not optimized for SAR data with respect to CCD.

We study all constacyclic codes of length 2sover GR(Rfr,m), the Galois extension ring of dimension m of the ringRfr=F2+uF2. The units of the ring GR(Rfr,m) are of the formsalpha, andalpha+ubeta, wherealpha,betaare nonzero elements of F2m, which correspond to2m(2m-1) such constacyclic codes. First, the structure and Hamming distances of(1+ugamma)-constacyclic codes are established. We then classify all cyclic codes of length 2soverGR(Rfr,m), and obtain a formula for the number of those cyclic codes, as well as the number of codewords in each code. Finally, one-to-one correspondences between cyclic andalpha-constacyclic codes, as well as(1+ugamma)-constacyclic and(alpha+ubeta) -constacyclic codes are provided via ring isomorphisms, that allow us to carry over the results about cyclic and(1+ugamma)-constacyclic accordingly to all constacyclic codes of length 2soverGR(Rfr,m).

Various kinds of distances of all negacyclic codes of length$2^{s}$over$\BBZ _{2^{a}}$are completely determined. Using our structure theorems of negacyclic codes of length$2^{s}$over$\BBZ _{2^{a}}$, we first calculate the Hamming distances of all such negacyclic codes, which particularly lead to the Hamming weight distributions and Hamming weight enumerators of several codes. These Hamming distances are then used to obtain their homogeneous, Lee, and Euclidean distances. Our techniques are extendable to the more general class of constacyclic codes, namely, the$\lambda $-constacyclic codes of length$2^{s}$over$\BBZ _{2^{a}}$, where$\lambda $is any unit of$\BBZ _{2^{a}}$with the form$4k-1$. We establish the Hamming, homogeneous, Lee, and Euclidean distances of all such constacyclic codes.

Codes over the ring of integers modulo 4 have been studied by many researchers. Negacyclic codes such that the length n of the code is odd have been characterized over the alphabet Zopf4, and furthermore, have been generalized to the case of the alphabet being a finite commutative chain ring. In this paper, we investigate negacyclic codes of length 2sover Galois rings. The structure of negacyclic codes of length 2sover the Galois rings GR(2a,m), as well as that of their duals, are completely obtained. The Hamming distances of negacyclic codes over GR(2a,m) in general, and over Zopf2ain particular are studied. Among other more general results, the Hamming distances of all negacyclic codes over Zopf2aof length 4,8, and 16 are given. The weight distributions of such negacyclic codes are also discussed

The structures of cyclic and negacyclic codes of length n and their duals over a finite chain ring R are established when n is not divisible by the characteristic of the residue field R~. Some cases where n is divisible by the characteristic of the residue field R~ are also considered. Namely, the structure of negacyclic codes of length 2/sup t/ over /spl Zopf//sub 2//sup m/ and that of their duals are derived.