Class Of Constant-weight Codes Research Articles

Constant Weight Codes From Constant Dimension Codes and Their Applications

This paper presents a geometric approach to the construction of constant weight codes from constant dimension codes. Two classes of constant weight codes are constructed based on the incidence structures in projective and Euclidean geometries, respectively. It is shown that some known optimal codes can be re-obtained in this way. As an application, the constructed codes are used in store-and-forward networks for packet loss recovery. Their decoding is translated into that of the corresponding constant dimension codes. The decoding capability is beyond that of the bounded-distance decoding. Remarkably, for constant weight codes from Koetter-Kschischang codes, the minimum-distance decoding is achieved.

Optimal Constant Composition Codes From Zero-Difference Balanced Functions

Constant composition codes are a special class of constant weight codes, and include permutation codes as a subclass. They have applications in communications engineering. In this correspondence, a generic construction of optimal constant composition codes using zero-difference balanced functions is introduced. It generalizes the earlier construction of optimal constant composition codes employing perfect nonlinear functions. In addition, two classes of optimal constant composition codes with new parameters are reported.

On a Class of Constant Weight Codes

For any odd prime power $q$ we first construct a certain non-linear binary code $C(q,2)$ having $(q^2-q)/2$ codewords of length $q$ and weight $(q-1)/2$ each, for which the Hamming distance between any two distinct codewords is in the range $[q/2-3\sqrt q/2,\ q/2+3\sqrt q/2]$ that is, 'almost constant'. Moreover, we prove that $C(q,2)$ is distance-invariant. Several variations and improvements on this theme are then pursued. Thus, we produce other classes of binary codes $C(q,n)$, $n\geq 3$, of length $q$ that have 'almost constant' weights and distances, and which, for fixed $n$ and big $q$, have asymptotically $q^n/n$ codewords. Then we prove the possibility of extending our codes by adding the complements of their codewords. Also, by using results on Artin $L-$series, it is shown that the distribution ofthe $0$'s and $1$'s in the codewords we constructed is quasi-random. Our construction uses character sums associated with the quadratic character $\chi$ of $F_{q^n}$ in which the range of summation is $F_q$. Relations with the duals of the double error correcting BCH codes and the duals of the Melas codes are also discussed.

Constant weight codes for correcting symmetric errors and detecting unidirectional errors

Proposes two classes of constant weight codes, which can be used for correcting t symmetric errors and simultaneously detecting all unidirectional errors. Codes in the first class are in quasi-systematic form and codes in the second class are in systematic form. Since each codeword of codes in both classes can be divided into a data part and a parity check part, the proposed codes have the merit of easily mapping messages into codewords.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>