An average Hamming weight enumerator is derived for the codewords at each Hamming distance from a received pattern in the set of all possible binary expansions of a Reed-Solomon code. Since these codes may be decoded by list decoders, such as those studied by Sudan (1997), the enumerator can be used to estimate the average number of codewords in the list returned by such a decoder.

In this paper, we present a new method of digital steganography, entitled spread spectrum image steganography (SSIS). Steganography, which means "covered writing" in Greek, is the science of communicating in a hidden manner. Following a discussion of steganographic communication theory and review of existing techniques, the new method, SSIS, is introduced. This system hides and recovers a message of substantial length within digital imagery while maintaining the original image size and dynamic range. The hidden message can be recovered using appropriate keys without any knowledge of the original image. Image restoration, error-control coding, and techniques similar to spread spectrum are described, and the performance of the system is illustrated. A message embedded by this method can be in the form of text, imagery, or any other digital signal. Applications for such a data-hiding scheme include in-band captioning, covert communication, image tamperproofing, authentication, embedded control, and revision tracking.

We present a new method of embedding information within digital images, called spread spectrum image steganography (SSIS). Steganography, which means "covered writing" in Greek, is the science of communicating in a hidden manner. SSIS conceals a message of substantial length within digital imagery while maintaining the original image size and dynamic range. The hidden message can be recovered using the appropriate keys without any knowledge of the original image. Image processing, error control coding, and spread spectrum techniques used to conceal the hidden data are described, and the performance of the technique is illustrated. The message embedded by this method can be in the form of text, imagery, or any other digital signal. Applications for such a data-hiding scheme include in-band captioning, hidden communication, image tamperproofing, authentication, invisible map overlays, embedded control, and revision tracking.

When a Reed-Solomon code is expanded to form a binary code, certain combinations of the spectrum of the Reed-Solomon code and the basis used for the expansion result in large gaps in the weight distribution of the binary code. It is shown that the size of these gaps can be bounded by computing the sums of various powers of the basis elements and applying a theorem normally used for cyclic codes. This explains why codes obtained by using a polymomial basis often have smaller gaps in their weight distributions than those obtained by using a normal basis. Similar results apply to the number of intersections between codewords, which can be used to show that the codewords are orthogonal.>

An explicit weight-enumerator for the set of binary expansions of a class of generalized Reed-Solomon codes is derived. This enumerator is then used to show that most of these binary codes are asymptotically good, and to bound the rates of self-intersecting codes.>

The author provides a simple method for determining the orthogonality of binary codes derived from Reed-Solomon codes and other cyclic codes of length 2/sup m/-1 over GF(2/sup m/) for m bits. Depending on the spectra of the codes, it is sufficient to test a small number of single-frequency pairs for orthogonality, and a pair of bases may be tested in each case simply by summing the appropriate powers of elements of the dual bases. This simple test can be used to find self-orthogonal codes. For even values of m, the author presents a technique that can be used to choose a basis that produces a self-orthogonal, doubly-even code in certain cases, particularly when m is highly composite. If m is a power of 2, this technique can be used to find self-dual bases for GF(2/sup m/). Although the primary emphasis is on testing for self orthogonality, the fundamental theorems presented apply also to the orthogonality of two different codes.>

Bounds on the rates of intersecting Goppa codes are derived and compared with previous bounds on intersecting codes. Intersecting, self-intersecting, and highly intersecting Goppa codes are discussed in detail. It is shown that asymptotically good intersecting Goppa codes exist and lower bounds are given on their rates. Six theorems for Goppa codes are also presented.>

Goppa codes exist arbitrarily close to the extended Varshamov-Gilbert bound for burst-correcting codes.

Goppa showed that the performance of most "Goppa codes" approaches the Gilbert bound asymptotically, but their performance for moderate lengths has not previously been demonstrated. In this correspondence, lower bounds are obtained on the minimum distance of most binary Goppa codes of any length.

It is shown that Goppa codes can be decoded by a simple modification of a decoder for a Reed-Solomon code.