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Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. Abstract— In this paper, we(More)
—In the present paper, we show that if the dimension of an arbitrary algebraic geometry code over a finite field of even characters is slightly less than half of its length, then it is equivalent to an Euclidean self-orthogonal code. However, in the literatures, a strong contrition about existence of certain differential is required to obtain such a result.(More)
It has been a great challenge to construct new quantum MDS codes. In particular, it is very hard to construct quantum MDS codes with relatively large minimum distance. So far, except for some sparse lengths, all known q-ary quantum MDS codes have minimum distance less than or equal to q/2 + 1. In the present paper, we provide a construction of quantum MDS(More)
The Reed-Muller (RM) code encoding n-variate degree-d polynomials over F q for d < q has relative distance 1 − d/q and can be list decoded from a 1 − O(d/q) fraction of errors. In this work, for d ≪ q, we give a length-efficient puncturing of such codes which (almost) retains the distance and list decodability properties of the Reed-Muller code, but has(More)
—There have been various constructions of classical codes from polynomial valuations in literature [2], [7], [8], [10], [11]. In this paper, we present a construction of classical codes based on polynomial construction again. One of the features of this construction is that not only the classical codes arisen from the construction have good parameters, but(More)
—It is well known that quantum codes can be constructed through classical symplectic self-orthogonal codes. In this paper, we give a kind of Gilbert-Varshamov bound for symplectic self-orthogonal codes first and then obtain the Gilbert-Varshamov bound for quantum codes. The idea of obtaining the Gilbert-Varshamov bound for symplectic self-orthogonal codes(More)