Virgilio Sison

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From a linear block code B over the Galois ring GR(4, m) with a k times n generator matrix and minimum Hamming distance d, a rate-k/n convolutional code over the ring Z<sub>4</sub> with squared Euclidean free distance at least 2d and a nonrecursive encoder with memory at most m - 1 is constructed. When the generator matrix of B is systematic, the(More)
In this paper, bounds are derived on the minimum homogeneous distance of the image of a linear block code over the Galois ring GR(p<sup>r</sup> ,m), with respect to any basis of GR(p<sup>r</sup>, m). These bounds depend on the parameters of GR(p<sup>r</sup> , m), the minimum Hamming distance of the block code, and the average value of the homogeneous weight(More)
Two constructions of unit-memory binary convolutional codes from linear block codes over the finite semi-local ring F2r + vF2r , where v = v, are presented. In both cases, if the linear block code is systematic, then the resulting convolutional encoder is systematic, minimal, basic and non-catastrophic. The Hamming free distance of the convolutional code is(More)
Let Fp be the prime field with p elements. We derive the homogeneous weight on the Frobenius matrix ring M2(Fp) in terms of the generating character. We also give a generalization of the Lee weight on the finite chain ring Fp2+uFp2 where u 2 = 0. A non-commutative ring, denoted by Fp2+vpFp2 , vp an involution in M2(Fp), that is isomorphic to M2(Fp) and is a(More)
In this paper, bounds are derived on the minimum homogeneous distance of the image of a linear block code over the Galois ring GR(p, m), with respect to any basis of GR(p, m). These bounds depend on the parameters of GR(p, m), the minimum Hamming distance of the block code, and the average value of the homogeneous weight applied on the base ring Zpr .(More)
Let p be a prime such that p ≡ 2 or 3 (mod 5). Linear block codes over the non-commutative matrix ring M2(Fp) endowed with the Bachoc weight are derived as isometric images of linear block codes over the Galois field Fp2 endowed with the Hamming metric. When seen as rank metric codes, this family of matrix codes satisfies the Singleton bound and thus are(More)
Let F2 be the binary field and Z2r the residue class ring of integers modulo 2 , where r is a positive integer. For the finite 16-element commutative local Frobenius nonchain ring Z4 + uZ4, where u is nilpotent of index 2, two weight functions are considered, namely the Lee weight and the homogeneous weight. With the appropriate application of these(More)
In coding theory, Gray isometries are usually defined as mappings between finite Frobenius rings, which include the ring Zm of integers modulo m and the finite fields. In this paper, we derive an isometric mapping from Z8 to Z4 2 from the composition of the Gray isometries on Z8 and on Z4 . The image under this composition of a Z8-linear block code of(More)