Optimal Ternary ( 10 , 7 ) Error - Correcting Codes

One-point Goppa Codes on Some Genus 3 Curves with Applications in Quantum Error-Correcting Codes

We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation yl = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x3 +x and Picard curves given by the equations y3 = x4-x and y3 = x4 -1. As a result, we obtain exact value of min...

Bounds for codes for a non-symmetric ternary channel

In [1], a non-symmetric ternary communication channel inspired by 3-valued semiconductor memories was introduced, and error-correcting coding for this channel was studied. The authors of [1] showed the relevance of the minimum d1-distance (defined below) of a ternary code for judging its error-correcting capabilities on this channel, gave a code construction, and derived a Hamming-like upper bo...

Separability of ternary codes for sparse designs of error-correcting output codes

Error-correcting output codes (ECOC) represent a successful framework to deal with multi-class categorization problems based on combining binary classifiers. With the extension of the binary ECOC to the ternary ECOC framework, ECOC designs have been proposed in order to better adapt to distributions of the data. In order to decode ternary matrices, recent works redefined many decoding strategie...

Ternary Error Correcting Codes and Fractionally Replicated Designs

On Perfect Ternary Constant Weight Codes

We consider the space of ternary words of length n and fixed weightwwith the usual Hamming distance. A sequence of perfect single error correcting codes in this space is constructed. We prove the nonexistence of such codes with other parameters than those of the sequence.